D. have
Either my aunt or my cousins have brought the potato salad to the barbecue. Makes sense right?
Try putting the other words in the sentence just to make sure :
Either my aunt or my cousins has brought the potato salad to the barbecue.
Either my aunt or my cousins was brought the potato salad to the barbecue.
Either my aunt or my cousins were brought the potato salad to the barbecue.
The only answer choice that makes sense is D. have.
Hoped I helped!