Quote Originally Posted by impulse View Post
Thanks for the example but I still do not understand the difference between Что and Как.
Sibiriak is very right, when he says that both versions are correct. in both cases, the semantics is the same:you ask someone about his opinion. The difference is in syntax, or in how you build your sentence after these two phrases.

When you start with "как ты думаешь", it functions as a parenthesis (i.e. an independent, isolated sentence), and has to be followed by another complete sentence that has the subject and the predicate. So you will end up with a compound sentence, in which you have two predications, two clauses:
(1) КАК ты думаешь , (2) эту книгу стОит читать?
(1) КАК ты считаешь , (2) моё предложение дельное?
(1) КАК ты полагаешь, (2) что будет дальше?"

However, when you start with "ЧТО ты думаешь.....", it already is the predication (I.e. the subject and the predicate), and that is why you have to add only the complement. in this case you end up with a simple sentence, with one predication:
"ЧТО ты думаешь об этой книге?
ЧТО ты думаешь по этому поводу?
ЧТО ты думаешь о моём предложении?