Here is the original item:
To get on his mother's good side,
(A) Rufus
offered to unpack the groceries,
(B) but dropped
the carton of eggs that Mom would later
need (C)
to make chocolate-broccoli muffins for the church bake sale.
You wanted to do this:
To get on his mother's good side, Rufus
offered to unpack the groceries, but dropped
the carton of eggs that Mom would later need,
to make chocolate-broccoli muffins for the church bake sale.
To put a comma after need is incorrect. To make chocolate-broccoli muffins for the church bake sale is an infinitive phrase. When a phrase of this type concludes a sentence, you do not need any punctuation.
You might want to review the rules.