Question

1. How many islands do you think Dokdo is made up of?

2. Do you think how many islands Dokdo is made up of?

(Is #2 incorrect? Why is that?)

Answer 1

Yes, 2 is incorrect. You could rephrase in any of these ways, depending on what you mean:

Do you know how many islands ... ?
Do you wonder how many islands ... ?
Do you think Dokdo is made up of more than ten islands?

There may be others, but these come to mind first!