Finite verbs are verbs that show agreement with the subject in terms of number and person. They are typically used in a sentence to indicate an action or a state of being. In this case, the finite verb is the verb that functions as the main verb in a sentence.

Among the given options, the finite verb is option C, "play". Let's break down the options to understand why the other options are not finite verbs:

a) playing: This is a present participle form of the verb "play". Present participles are verb forms that end in -ing and are used to form continuous tenses. However, they do not function as the main verb in a sentence.

b) to play: This is an infinitive form of the verb "play". Infinitives are verb forms that are used to express purpose or intention. They are not finite verbs because they do not agree with the subject in terms of number and person.

d) plays: This is a present tense form of the verb "play" that agrees with the third-person singular subject. Although it is a finite verb, it is not the correct answer in this case because it is in the third-person singular form and does not agree with the subject of the sentence.

Therefore, option C, "play", is the correct answer as it is a base form of the verb that can function as the main verb in a sentence and agree with the subject in terms of number and person.

To summarize:

- Finite verbs show agreement with the subject in terms of number and person.
- Option C, "play", is a finite verb because it functions as the main verb in a sentence and agrees with the subject.
- Options a) and b) are not finite verbs as they are in the present participle and infinitive forms, respectively.
- Option d) is a finite verb, but it does not agree with the subject.