I enjoy ________ stories for children.

The correct verb form to complete the sentence is Writing.
Write - is a wrong answer because 'write' is the base form of the verb and the given sentence is in the continuous tense, thus the verb should follow the same pattern, i.e., continuous action.
To write is an incorrect answersince 'to write' is not a continuous form.
Writing - is the correct answer since 'writing' is the continuous form of the verb and the verb 'writing' refers to the act of continuously feeling something, i.e. the feeling of writing.
Having been writing - is an incorrect answer since 'having been writing' is grammatically inaccurate and completely unsuited in the sentence.