Hi Jasmine There's no difference - 'you don't say nothing' is a slang way of saying 'you don't say anything'

That's very interesting. Perhaps in colloquial English quite a few sentences are traditionally accepted and in no need of studying its logical meaning.

you don't say anything: 你什么都不说 you don't say nothing: 你不会什么都不说/你一定会说

In English, a double negative makes a positive. "You don't say nothing" means "you do say something", which is the opposite of "you don't say anything". However, the difference disappears in colloquial speech, as Neal pointed out.

"You don't say anything" is the correct way to say that. Yeah, double negatives make the sentence positive and I guess that is the difference between those two sentences, so there's the answer to the question. However, (well in America anyway) "You'don't say nothing" is not the proper way to speak. Double negatives are incorrect. English teachers across America have to shudder when they hear double negatives. Besides, it is confusing to speak that way.