The reason for this word order is that the question is a subject-question. The answer is the subject of the sentence containing the answer. e.g. Who (do you think) is knocking on the door ? (I think) Bob is knocking. You might also see this word order in a passive question e.g. Who (do you think) should be given the job of clearing the garage?

If I ask someone, "What do you THINK about global warming", I am asking for their opinion or VIEWPOINT. They might answer, "In my opinion, it is a major problem". In contrast, If someone asks, "How do you FEEL about global warming". They might describe their emotions. They might answer, "It frightens me to read some reports". If someone asked me, "What do you THINK is the best way to stay healthy", I would give my viewpoint, "I AGREE with most experts who say we need regular exercise, healthy(healthful) food and a proper amount of sleep". Hope this is some help to you.

I do not follow your question, sorry. . I think the question can be answered. I think the question can be answered in more than one way. I think this is the best way to answer the question. What do you think is the best way to answer the question? . It asks what you think/believe to be ... something... . What do you think about Trump? What do you think of Trump? What do you think about Brexit? What do you think is the best way to resolve the Brexit fiasco? . There are many ways to get to school. What do you think is the best way? What do you think is the best way to get to school. Please give me your view of what is the best way to get to school. . Hope this helps. Which do you think is the best answer so far? Do you think it best to wait for more answers? Another one may be just what you need.