Take a look at the item again:
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.
Go back to the sentence to try again.