The correct answer and the type of compound contained by the sentence "Tomas reads and writes piano music" is C) compound verb.
Compound verbs are made of more than one word. Some examples of these are phrasal verbs, prepositional verbs, a verb with auxiliaries or compound single-word verbs.
In the mentioned sentence, the subject is capable of doing both actions related to the same object. We have just one single subject, Tomas, and just one object piano music. On the other hand there is a compound verb reads and writes because Tomas can do both.