Question

either of the teams proves₁ prove₂ a worthy opponent for the defending state champion.
option 1: proves
option 2: prove

Explanation:

In the sentence "Either of the teams proves/prove a worthy opponent for the defending state champion", the subject is "Either of the teams". "Either" (when referring to one of two) takes a singular verb. So "proves" (singular verb form) is correct, while "prove" is plural and incorrect here.

Answer:

Option 1: proves