Final answer:
The verb that correctly fills in the blank is 'has'. The correct answer is option b.
Step-by-step explanation:
The correct verb to fill in the blank in the sentence 'Either my sister or my brother _____ my math textbook' is has.
When using either/or or neither/nor to connect two subjects, the verb should agree with the subject closest to it. In this sentence, the subject closest to the verb is 'brother,' which is singular, so the verb should be singular as well.
Example: Either my sister or my brother has my math textbook.