The correct option is C What
The correct answer is Option D.
WHAT is used when we want to know about some thing. In the given sentence the speaker wishes to know of the father's activity in his free time. Therefore, WHAT is the correct word that completes the sentence.
The remaining options are incorrect because:
Option A: WHY is used to know the reason.
Option B: WHAT KIND is used to determine the nature of something.
Option C: HOW MUCH is used to determine the quantity of something.
Hence Option D is the correct answer.