“And it came to pass on the eighth day, that Moses called Aaron and his sons, and the elders of Israel;”
After their consecration: for the seven days before, the Priests were consecrated.
“And he said unto Aaron, Take thee a young calf for a sin offering, and a ram for a burnt offering, without blemish, and offer them before the LORD.”
Aaron entereth into the possession of the Priesthood: and offereth the four principal sacrifices, the burnt offering, the sin offering, the peace offerings, and the meat offering. Cross references: : Exod. 29:1
“And they brought that which Moses commanded before the tabernacle of the congregation: and all the congregation drew near and stood before the LORD.”
Before the Altar where his glory appeared.
“And Moses said unto Aaron, Go unto the altar, and offer thy sin offering, and thy burnt offering, and make an atonement for thyself, and for the people: and offer the offering of the people, and make an atonement for them; as the LORD commanded.”
Read for the understanding of this peace, Heb. 4:5 and 7:27.
“But the fat, and the kidneys, and the caul above the liver of the sin offering, he burnt upon the altar; as the LORD commanded Moses.”
That is, he laid them in order, and so they were burnt when the Lord sent down fire.
“And he did wash the inwards and the legs, and burnt them upon the burnt offering on the altar.”
All this must be understood of the preparation of the sacrifices which were burnt after, verse 24.
“And Aaron lifted up his hand toward the people, and blessed them, and came down from offering of the sin offering, and the burnt offering, and peace offerings.”
Because the altar was near the Sanctuary, which was the upper end, therefore he is said to come down.
“And there came a fire out from before the LORD, and consumed upon the altar the burnt offering and the fat: which when all the people saw, they shouted, and fell on their faces.”
Or, gave a shout for joy. Gen. 4:4 ; 1 Kings 18:38 ; 2 Chron. 7:1