But God graciously did the necessary hiding and covering of their guilt and shame with the "coats of skins" according to Gen. 3:21. It is significant to remember that the word "skins" in the KJV is plural, but in the original it was singular. This is important, perhaps, because, as C. W. Slemming says, "This suggests that one sacrifice was sufficient for both."
It is also significant to remember that this is the first example of a" Kethoneth" needed to cover man's sin and to hide man's shame. It wasn't a Botany 500 [the best suit back in my day of buying suits] that Adam now wore, but it sure was a fine garment of a totally different nature for both he and his wife.
The first High Priest for Israel was another example of wearing a wonderful garment. It was a "coat" [there's that word kethoneth again] made of "fine linen" according to Exodus 18:39. Aaron, the High Priest, wore it as an inner garment but his sons, the Priests, wore it as their only garment. [Plus the Priestly girdle, bonnet etc.]
With this coat the High Priest and the Priests were sufficiently covered so they could minister in the Tabernacle itself. Then, on that wonderful day of Atonement, the High Priest would by himself, take in the blood of the lamb, sprinkle it on the mercy seat, which covered the law that was in the Ark of the covenant, and sinful man had an audience with God. More than an audience...man had relationship with God.
We know the blood speaks of His sacrifice for us on the Cross. He gave His life on our behalf. But often forgotten is the righteousness that is His which is imputed to us by Grace. You see that "coat of linen" speaks of our guilt and shame being hidden once and for all. Isaiah foretold of it with these words, "I will greatly rejoice in the Lord, my soul shall be joyful in my God: for He hath clothed me with the garments of salvation, He hath covered me with the robe of righteousness..." [Isaiah 61:10]
I'm sure we all agree that Righteousness was the foundation of everything Christ was and did. But our claim to being righteous is of a different nature. It is not our own. It is a righteousness given to us by Him. So our High Priest, the Lord Jesus Christ, who is righteous in His very character, [As shown by the inner garment of the High Priest] is willing that His righteousness become imputed to us. [As shown by the outer garment of the Priests.] All this so that we are, in fact, clothed with His Righteousness, because we are washed in His blood, and as Adam pictured, we are free from EVER being seen in our guilt and shame.
Not a botany 500 by any means. Far better than that. Our garment is a permanent covering. THAT, my friend, is GRACE.