Then: or “Afterwards,” or “After that” (Good News Translation), or “Next…” (New Jerusalem Bible). New American Bible has “Thereupon….” Most versions also begin a new paragraph at this point.
He: it may be important is some languages to specify Aaron in place of the pronoun in this case. This is especially true in those cases where this verse starts a new paragraph.
The people’s offering: Good News Translation takes the first part of this verse as a separate sentence and a kind of introduction to the section that follows. For this reason it has the plural “offerings,” which refers to the various offerings mentioned in the verses that follow. However, most versions retain the singular offering, which then refers only to the sin offering in this verse.
Like the first sin offering: this refers to the offering Aaron had previously made for his own sin (see verse 8). In some cases one may say “as he had done with the calf (or, bull).”
Quoted with permission from Péter-Contesse, René and Ellington, John. A Handbook on Leviticus. (UBS Helps for Translators). New York: UBS, 1990. For this and other handbooks for translators see here .
