Final answer:
The sentence in question is a simple sentence because it contains one independent clause with a subject and a predicate.
Step-by-step explanation:
The sentence "After the hurricane, many of the offices needed new carpeting." is a simple sentence. A simple sentence has only one independent clause and no dependent clauses. In this case, the independent clause is the entire sentence, which contains a subject ('many of the offices') and a predicate ('needed new carpeting').