Question

1. Do you quietly think so?
2. Do you really think so?
3. Do you easily think so?
4. Do you finally think so?

5. He solved the math problem very quietly.
6. He solved the math problem very really.
7. He solved the math problem very easily.
8. He solved the math problem very finally.
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Which ones are unacceptable?

Answer 1

6 and 8 are unacceptable. The others are good. If he solved the math problem, then he really solved it; there's no need to add "really", much less "very really". It's either real or it's not; no modifier is needed. The same goes for "finally".

Answer 2

I think #s 1, 3, and 4 are awkward. #2 is a rather common expression, but I've never read or heard the others.

I agree with Reed about #s 5-8.