Which is more correct to say as quick you can or quickly can?

Neither "as quick you can" nor "quickly can" is grammatically correct. The correct phrase is "as quickly as you can".

Here's why:

* "As quick you can" is missing a necessary word ("as") to make the phrase grammatically sound.

* "Quickly can" is also incorrect because "quickly" is an adverb and "can" is a modal verb. They cannot be used together in this way.

"As quickly as you can" uses the comparative adjective "quickly" in a comparative structure, making it the correct and natural way to express this meaning.