Hello, I think I have an idea of why you might be confused by "how do you think" vs "what do you think", you can use "do you think" to make a question less direct. "think" and "suppose" are interchangeable, and the question word (who/what/where/why/when) comes from the original question: "What will they do to fix the economy?" => "What do you think they will do to fix the economy?" 経済を直すために何をしますか？　＝＞　経済を直すために何をするでしょうか？／何をすると思いますか？ "Where did he go last week?" => "Where do you think he went last week?" 先週どこに行きましたか？　＝＞　先週どこに行ったでしゅうか？ "How will they fix the economy" => "How do you think they will fix the economy?" "When will dinner be ready?" => "When do you think dinner will be ready?" "Why did he leave" => "Why do you think he left?" You can replace "do you think" with "do you suppose" in any of these ("where do you think they went?", "where do you suppose they went?"). I think it's a dialect thing, I almost always use "think". Someone speaking the American Southern dialect might use "reckon" ("Where do you reckon they went?")

Let's consider the following expressions: 1. How do you suppose, you are going to solve this problem? 2. How do you suppose, you are going to find a solution to this problem? ** (here the possible "ways" to the "solution/s" are presumably more than one. The person who asks you this question is in fact asking you to consider all these possible "ways" to find a "solution" and then to choose one or the other. So, here the emphasis is more on the "logical ways to solution/s" rather than on the actual "solution" itself.) ------------------------------------------------------------ 3. What do you think about the possible solution/s to this problem? 4. What do you think, the possible solution/s to this problem should be? ** (here the person wants to know about the possible "solution/s" to the problem. Emphasis is more on the "solution" rather than on "ways". You may arrive at multiple "solutions" by following multiple logical "ways"..... but, the person who asks you this question is definitely NOT interested in those "logical ways to the solution/s". Only the "solution" (that you can think of) is all what he wants to know about.)

あなたはどのように思いますか?

You use 'how' and 'what' in different context. 'How' is used to enquire about in the way or manner for example; How does the car work? or How would I get to the shop? What is used when requesting specific information or used to specify a person for example; What is she doing? or What does the shop sell? Also; 'think' and 'suppose' are similar in there meaning although 'suppose' is used more when the person is not sure or is guessing. What do you think? What do you suppose? How do you think? How do you suppose? You can use any of the above to ask a question, the key word is 'What' and 'How' if you get this wrong the sentence will not sound right. Its hard to explain but practice your speech as much as possible and you will get a feel for what is right. Hope that helps. Paul