Albert Barnes Commentary Leviticus 16:6

"And Aaron shall present the bullock of the sin-offering, which is for himself, and make atonement for himself, and for his house." — Leviticus 16:6 (ASV)

Shall offer - Rather, shall present, as in Leviticus 16:7, Leviticus 16:10, etc. The word expresses the formal act of placing the victims in front of the entrance of the tabernacle.

For himself, and for his house - that is, for himself as the high priest and all the common priests. Compare Leviticus 9:7-14 note.