Final answer:
The sentence 'Either the walnuts or the vanilla extract adds just the right flavor' has a compound subject of 'the walnuts' and 'the vanilla extract', with 'the vanilla extract' being the part that influences the singular verb 'adds'.
Step-by-step explanation:
In the sentence "Either the walnuts or the vanilla extract adds just the right flavor," we are dealing with a sentence that has a compound subject joined by the conjunction 'or'. In such cases, the verb should agree with the part of the subject closer to it. As 'vanilla extract' is singular and closer to the verb, it dictates that 'adds' is the correct singular verb form. Thus, the subjects in this sentence are 'the walnuts' and 'the vanilla extract', but 'the vanilla extract' is the part that is influencing the verb agreement.