The sentence with correct pronoun and antecedent agreement is:
While the neighbors were walking to the store, they dropped their money and the wind blew it away.
In this sentence, the pronoun "they" correctly agrees with the plural antecedent "neighbors." The other options have issues with pronoun-antecedent agreement. For example, "he" in the first option does not agree with the plural "brothers," and "she" in the last option does not agree with the plural "teachers."