The correct option is
D visiting
Answer : A
In the sentence, "My Children" is the Subject, "enjoy" is the verb and Object is "places".
The structure of the sentence is that of Active Voice, i.e. Subject + Verb + Object. The subject is directly acting on the object.
And according to the grammar rules, some verbs are followed by the gerund form of the verb. One such verb is "visit".
The gerund form can be made by adding "ing" to the base form of the verb.
Here, the gerund form of the verb "visit", is "visiting".
And thus, the correct complete sentence is:
I enjoy VISITING places I've never been to before.