What is the difference between why don't you and why you don't?

Answer 1

"why don't you?" is a question.

"why you don't" is a command.

Why you don't? is not a correct question. Also it is not a command.

Why can be used to give a suggestion or piece of advice eg.

'Why don't you sell your car by advertising it in the paper?'

I think 'why you don't' is a variation on this usage eg

'Why you don't sell that car I'll never know'

Answer 2

"Why don't you" is a polite way to suggest or ask someone to do something. "Why you don't" is not a grammatically correct phrase.