The verb is used with 's/es' at its end when the noun/pronoun is singular and the sentence is in the simple present tense. The verb is used without 's/es' with plural nouns in the simple present tense. The sentence is given in simple present tense and the subject is singular (He). Therefore, the correct option is: likes to do nothing.
Another possible answer is C) doesn't like to do anything. Here, we use the negative sentence which takes the form 'doesn't'+ base form of verb for singular subjects like he, she and it.