Final answer:
The sentence should be 'Neither of my brothers likes loud music' because 'neither' is treated as a singular subject, requiring a singular verb for correct subject-verb agreement.
Step-by-step explanation:
The question pertains to subject-verb agreement in English grammar. When determining the correct form of the verb, it is important to identify the subject and whether it is singular or plural. In the sentence 'Neither of my brothers like/likes loud music,' the subject is 'Neither of my brothers,' which is considered singular, so the correct verb form should be 'likes'.
Subject-verb agreement is a fundamental rule in English that dictates that a singular subject takes a singular verb, while a plural subject takes a plural verb. The word 'neither' when used as a subject is always treated as singular, which is why 'likes,' the third person singular form of the verb 'like,' is the appropriate choice.