Answer: "I need to clean up his kitchen."
"Before my brother comes home, I need to clean up his kitchen.”
Explanation: The independent clause within the sentence is "I need to clean up his kitchen," for the clause can exist on its own and still make sense. The beginning of the sentence, "Before my brother comes home," is your dependent clause. If this clause was not accompanied by your independent clause, the sentence would be incomplete.
Think of the keywords here as independent and dependent. The independent clause can exist independent of the dependent clause, while the dependent clause is reliant on the independent clause to create a complete sentence.