Concept:When the verb
like is used to talk about enjoying an activity in general, it is followed by the
-ing form (gerund) of the next verb.
Explanation:The sentence is a general statement: she does not enjoy the activity of writing letters.
The gerund of
write is
writing, so "writing letters" is the object of
like: "She does not like writing letters."
The base verb
write cannot follow
like directly.
"to writing" is wrong: after
like,
to is followed by the base verb, not the
-ing form.
"to be writing" (continuous infinitive) does not fit a simple general statement like this.
Key point: The printed option B was "to write". "She does not like to write letters" is also correct English, so two options were right. Option B has been changed to "to writing" so that only one answer fits.
Answer:Option D (writing)