BY FAITH WE UNDERSTAND THAT THE WORLDS WERE PREPARED BY THE WORD OF GOD: Pistei nooumen (1PPAI) kathertisthai (RPN) tous aionas rhemati theou,: (24x in this chapter): (1:2; Genesis 1:1-31; 2:1; Psalms 33:6; Isaiah 40:26; Jeremiah 10:11,16; John 1:3; Acts 14:15; 17:24; Romans 1:19-21; 4:17; 2 Peter 3:5; Revelation 4:11)

Each ex of faith in v 3-31 is formally introduced with this specific phrase=> pistei. Instrumental case of pistis True saving faith equates with obedience to God (Ja2:14-26).

There are two explanations for the origin of this universe. One is speculation, and the other is revelation. By faith we accept revelation, and, my friend, by faith you will accept speculation.

Understand - perceive w thought coming into consciousness as distinct from the perception of senses. Perceiving clearly with the mind, of understanding fully, Mt15:17; Ro1:20 (have been clearly seen, being understood through what has been made)

Vincent says

“Here is meant the inward perception and apprehension of the visible creation as the work of God, which follows the sight of the phenomena of nature.”

The physical universe itself, as well as its operation and administration. The "age" of time and space in which people now live and have lived since the world was drastically changed by the Flood in the days of Noah.

Alford says that the expression “includes in it all that exists under the conditions of time and space, together with those conditions of time and space themselves, conditions which do not bind God, and did not exist independently of Him, but are themselves the work of His word.”

Prepared (KJV = "framed" like framers of a house). The concept involved in this verb (v13:21) is that of equipping so that something might be made ready to fulfill its purpose. word of God. God’s divine utterance (Ge1:3,Then God said, "Let there be light"; and there was light. Ge1:6,9,11,14). (Lu 6:40 =has been fully trained)

The word “word” is not the translation of logos (logo") as in Jn1:1, logos being a designation of the Son of God as the Word of God in the sense that He is in Himself all that deity is, deity expressing itself not in words as parts of speech, but in the revelation of a Person. It is the translation of hrema (rJema) which speaks of articulate utterance. This word is never used as a designation of God the Son. It is the Word of God to which reference is made here, not the Son of God. God spoke the word, and a universe sprang into existence.

Ultimately the Word is Jesus, the Creator and Sustainer (Col 1:16,17), Who is called this phrase ''The Word (here ''logos'') of God'' in Rev 19:13. The phrase “and God said” occurs nine times in Ge1:4. “For He spake, and it was done; He commanded, and it stood fast” (Ps 33:9)

SO THAT WHAT IS SEEN WAS NOT MADE OUT OF THINGS WHICH ARE VISIBLE: eis to me ek phainomenon (PMPNPG) to blepomenon (PPPNSA) gegonenai (RAN):

Since the universe was framed by the word of God, it follows, the writer argues, that that which is seen was not made out of that which is visible.

Adam and Eve are passed over in this portion regarding creation because they had seen God, fellowshipped with Him, and talked with Him. Their children were the first to exercise faith in the unseen God but also the first to commit murder.

BY FAITH ABEL OFFERED TO GOD A BETTER SACRIFICE THAN CAIN: Pistei pleiona thusian Abel para Kain prosenegken (3SAAI) to theo: (Genesis 4:3-5,15,25; 1 John 3:11,12) (9:22; Proverbs 15:8; 21:27; Titus 1:16; Jude 1:11) 

To bear or bring to a place or person. gifts (Mt2:11; Used in Lxx to describe Cain = Ge4:7

Literally, "more sacrifice" (comparative of polus, much). It is a mistake to read into this Genesis account any hidden reasons for God’s acceptance of Abel’s offering and rejection of Cain’s.

Various explanations have been offered, but the writer is silent about everything except that God “spoke well” of Abel’s offering because it was “better”= pleiona =“greater” “more important” as suggested by its use in Lu12:23: “Life is more than food, and the body more than clothes.”

If Abel’s sacrifice was more important than Cain’s, what made it so? The reason suggested is that it was OFFERED UP from a heart made righteous BY FAITH! If Abraham’s FAITH was “credited to him as righteousness” (Ro4:9), so also was Abel’s. So Abel performed a "RIGHTEOUS" work, an acceptable sacrifice pleasing to God in the only manner anyone can please God -- "BY FAITH" (cp 11:6).

Ge 4:7 indicates that when Cain learned that his offering was not pleasing to God (Heb11:6) he became angry and rebellious, thus confirming the attitude of His heart toward the sovereign will of God. But even in Ge4:7 God provided a "way of escape" so to speak...reflecting God's heart that no man perish but that all come to repentance (2Pe3:9). Cain’s subsequent murder of his brother showed his stubborn rejection of the opportunity God gave him to repent and to offer again, presumably with a contrite spirit.

Cain’s offering was rejected because a heart of pride and self-sufficiency lay behind it. This explanation fits well with the context of Hebrews where the writer repeatedly warns against possessing “an evil heart of unbelief.”

Abel’s offering was ''BETTER'' not just because it was an animal, nor just because it was the very best of what he had, nor even that it was the culmination of a zealous heart for God; but, because it was in every way obediently given according to what God must have revealed (though not recorded in Genesis). Cain, disdaining the divine instruction, just brought what he wanted to bring: some of his crop.

THROUGH WHICH HE OBTAINED THE TESTIMONY THAT HE WAS RIGHTEOUS GOD TESTIFYING ABOUT HIS GIFTS AND THROUGH [IT], THOUGH HE IS DEAD, HE STILL SPEAKS: einai (PAN) dikaios marturountos (PAPMSG) epi tois dorois autou tou theou marturountos (PAPMSG) epi tois dorois autou tou theou kai di autes apothanon eti lalei (3SPAI): (Leviticus 9:24; 1 Kings 18:38; Matthew 23:35; Luke 11:51)  (12:1,24; Genesis 4:10; Matthew 23:35 )

Note "martureo" used 4x in Hebrew 11 (11:2, 4,5, 39) So Abel was JUSTIFIED BY FAITH. He is here on the authority of God's word, declared righteous and that righteousness was imputed or credited to his account on the basis of his FAITH, not on the basis of his offering. His "better offering" was the work of faith. Faith alone saved Abel but his saving faith was not alone but was an obedient faith that resulted in a "better sacrifice".

Because of Abel's faith, evidenced in obedience to God’s requirement for sacrifice, he was accounted as righteous by God (Ro 4:4-8). Christ Himself referred to the righteousness of Abel (Mt23:35). Cain’s sacrifice was evidence that he was just going through the motions of ritual in a disobedient manner, not evidencing authentic faith. Without faith no one can receive imputed righteousness (Ge 15:6).

Romans 4:4 "Now to the one who works (CAIN), his (CAIN's) wage is not reckoned as a favor, but as what is due.5 But to the one (ABEL) who does not work, but believes in Him who justifies the ungodly, his (ABEL's) faith is reckoned as righteousness"

So Cain was saying in essence to God...in my own strength & effort, I can produce a righteousness which will obtain Your approval...WRONG! In our flesh their DWELLETH NO GOOD THING! We all need to be mindful of this effect of the fall...we must continue to live this Christ life just as we were born into it...BY FAITH!!! (Col 2:6) Also see [12:24], in which still another reference is made to the nature of Abel's sacrifice.

Like MOST early Christian exegetes, Augustine treats Cain as symbolic of the envious “Jews by whom Christ was slain,” while Christ himself, “the shepherd of the flock of men, [is] prefigured in Abel, the shepherd of the flock of sheep” (De civ. Dei 15.7; cf. 15.18). This is taking considerable liberty with what the text actually says. It is loose exegesis like this that probably underlies much of the justification for so-called "replacement" theology wherein the church is tragically & wrongly interpreted as having replaced the literal nation of Israel (and the literal Jewish race) and now stands as the heir of God's OT promises to Israel. (but see God's evaluation of "replacement" theology Jer 31:35, 36, 37)

BY FAITH ENOCH WAS TAKEN UP SO THAT HE SHOULD NOT SEE DEATH: Pistei Enoch metetethe (3SAPI) tou me idein (AAN) thanaton: (Genesis 5:22-24; Luke 3:37; Jude 1:14 ) (Genesis 5:22-24; Luke 3:37; Jude 1:14 )

Enoch is an example to the readers of Hebrews of what the writer longed to see happen to them: a steady, daily growth in grace achieved by the inner resources which God supplies to those who take him at his word and act in faith on what he has said. Enoch enjoyed the continuous presence of an unseen Person, and related his life daily to that Person. The result was a fellowship which death could not interrupt.

Taken up (3331) (metathesis from metatíthemi = transfer from meta  = implying change + tithemi = put) is literally, the act of transferring from one place to another  and so the removal or taking up or away. And so it can describe a transfer from one place to another, as for example the translation of a person to heaven as in this verse.

Hebrews 12:27 uses metathesis with the idea of removal.

And this expression, "Yet once more," denotes the removing of those things which can be shaken, as of created things, in order that those things which cannot be shaken may remain.

Figuratively, metathesis means to transpose or put one thing in the place of another. It can mean a change of things instituted or established, such as a changeover from the Levitical priesthood

For when the priesthood is changed, of necessity there takes place a change of law also. (Hebrews 7:12)

Transliterated it gives us the English word metathesis which is defined as the transposition of a letter of a word.

Vincent comments on the meaning of metathesis here in Hebrews 7:12 writing that it refers to

A change. A transfer to a new basis. Only in Hebrews. See notes Hebrews 11:5; Hebrews 12:27. The inferiority of the Levitical priesthood is inferred from the fact that another priesthood was promised. If perfection was possible at all under the Mosaic economy, it must come through the Levitical priesthood, since that priesthood was, in a sense, the basis of the law. The whole legal system centered in it. The fundamental idea of the law was that of a people united with God. Sin, the obstacle to this ideal union, was dealt with through the priesthood. If the law failed to effect complete fellowship with God, the priesthood was shown to be a failure, and must be abolished; and the change of the priesthood involved the abolition of the entire legal system.

AND HE WAS NOT FOUND BECAUSE GOD TOOK HIM UP FOR HE OBTAINED THE WITNESS THAT BEFORE HIS BEING TAKEN UP HE WAS PLEASING TO GOD: kai ouch heurisketo (3SIPI) dioti metetheken (3SAAI) auton o theos kai ouch heurisketo (3SIPI) dioti metetheken (3SAAI) auton o theos. pro gar tes metatheseos memarturetai (3SRPI) euarestekenai (RAN) to theo: (2 Kings 2:16,17; Jeremiah 36:26; Revelation 11:9-12) (6; Genesis 5:22; Romans 8:8,9; 1 Thessalonians 2:4; 1 John 3:22)

Two important things mark the character of Enoch’s faith: (1) he pleased God by turning away from the godlessness of the world in which he lived and (2) he maintained a daily walk with God which grew so intimate that he was taken to heaven without experiencing death.

The Genesis account (Gen 5:21–24) indicates that for the first 65 years of his life, Enoch did not walk with God. Presumably he went along with the deteriorating morality of his times, which Genesis 6:5 describes. As Ge5:25 suggests, the event which changed Enoch’s outlook was the birth of a son, whom he named Methuselah. Some scholars derive the meaning of Methuselah from the Hebrew root muth, which means “death,” and translate the name “His death shall bring (it).”