what do you think they should do to solve their problems

这个句子也可以这样理解.
To solve their problems,what do you think they should do?
或者
To solve their problems,do you think what should they do?
你认为他们应该怎样做才能解决到问题?
To solve their problems,表达目的,目的是解决他们所遇到的问题.
What do you think they should do.表示让步的询问.