Charles Ellicott Commentary Leviticus 16:24

"and he shall bathe his flesh in water in a holy place, and put on his garments, and come forth, and offer his burnt-offering and the burnt-offering of the people, and make atonement for himself and for the people." — Leviticus 16:24 (ASV)

And he shall wash his flesh. —That is, immerse his whole body. The baptistery, where the high priest performed these ablutions, was on the roof of a building in the sacred precincts. According to the authorities and practice during the Second Temple, the act described in this verse preceded the one ordered in the previous verse.

The burnt offering, both for himself and for the people, the high priest offered in the golden garments. These he changed for the white robes when he afterwards went into the Holy of Holies to fetch the censer and the incense cup. The sacrifice consisted first of his own ram, then the ram of the people, and lastly the bullock of the people, and their seven lambs .