Answer: C) would have worked.
Explanation: A verb phrase is a syntactic unit consisting of an auxiliary or helping verb preceding the main verb. In the given sentence, the verb phrase is "would have worked" as we can see, the main verb is "worked" (it indicates the action that is being performed) and the auxiliary verbs are "would have." In the rest of the sentence we can see that "my brother" is the subject and "all summer" is a complement.