Right answer: visitaron
This is a sentence written in simple past tense. We are able to know this because of the word ayer (yesterday).
Note, in spanish (castillian) the Simple Past Tense is used to express specific actions completed or concluded in the past that are separated from the present.
This means, it is applied when the person speaking gives information about the past that is not related to the present.
Now, the subject in the sentence is mi prima y mi hermano (my cousin and my brother) which is the 3rd person in plural ellos (they). Hence the correct conjugation of the verb visitar (to visit) in past with this subject is visitaron (they visited), and the complete sentence is:
Ayer, mi prima y mi hermano visitaron la biblioteca municipal.
Yesterday, my cousin and my brother visited the municipal library.
The other options are incorrect because:
-visité (I visited) although is conjugated in simple past, it is written with the 1st person in singular yo (I). Thus, it does not match with the subject of the sentence.
-visitan (they visit) is written in present tense with the 3rd person in plural ellos (they).
-visitó (he/she visited) although is conjugated in simple past, it is written with the 3rd person in singular él/ella/eso/esa (he/she/it). Thus, it does not match with the subject of the sentence.