The correct answer is: She enjoys playing tennis. This is an example of a verb that is followed by a gerund - the 'ing' form of the verb. On the other hand a verb such as 'hope' takes the infinitive form of the verb:
She hopes to visit her parents soon.
Unfortunately, as is the case with irregular verbs, there is no fixed rule for knowing whether a verb takes a gerund or the infinitive. You can improve your understanding by using this gerund or infinitive tool to check and by testing your knowledge with this interactive quiz.