Translation:What do you think, is there a school here?
My take on this is that the correct translation for that would be "как ты думаешь, школа есть здесь", on the base that usually the least known part is last in the sentence, so in your case you know there is a school, just don't know where, but in the exercise they don't know if there is a school at all. Any native can confirm my thoughts? Sorry for mistakes
This is a good question. I thought of different situations when I would say "как вы думаете" and "что вы думаете", and here are my ideas:
We usually say как вы думаете when we ask about some alternatives:
- Как ты думаешь, завтра будет дождь? Do you think it will rain tomorrow? (There are two alternatives, whether it will rain or won't.)
- Как вы думаете, он согласится? Do you think he will agree?
We can also use "Как ты думаешь?" to urge someone to think and give their guesses:
- Знаешь, кто ко мне вчера приходил? - Do you know who visited me yesterday?
- Понятия не имею. - No idea.
- Ну, как ты думаешь? - Come on, have a try / Well, what do you think?
We usually say что вы думаете when we are asking to express thoughts and opinions:
- Что ты думаешь об этом предложении? What do you think about this proposal?
- Что вы думаете по этому поводу? What are your thoughts on this matter?
Maybe other native speakers will add more examples.
Not a native.... but i asked my jative wife. She agrees with what Olima has stated and added that "что" is usually, if not always linked with "о" or a similar preposition, leaving it more open ended where as "как" follows the rules/patterns like Olima provided.
Another use of "что"without such a preposition is a kind of aggressive questioning, challe ging your view.
Not sure how much that helps, but trying to expand the understanding of this difficult russian nuance как думаешь - что думаешь
Non-native, so I could be wrong, but I believe the есть in this sentence implies that the question regards the existence of a school, so "What do you think, is there a school here?" is more a more accurate translation than "What do you think, is the school here?" because the latter sentence assumes that there is a school somewhere, while the former asking if one exists at all. It seems like a minor difference but the two are definitely different questions.