我看不知道,我觉得还是
what do you like doing

what do you like doing?

都行，但是What do you like doing ?精确一点

what do you like doing?

what do you like?

两个都可以，但是what do you like doing?指向性更强些

What do you like doing? 因为这是对划线部分提问，也不能用 Do you have any hobbies? 因为这句话的回答是 Yes, I do. 这是个一般疑问句，不是特殊疑问句。

我认为应该是what do you like doing

我觉得应该是what do you like?

我认为应该是what do you like doing?
这是服从原句。