In Shakespeare’s time, double negatives such as can’t hardly were common, but in current standard usage (and by current, I don’t mean that I just made it up this week!), double negatives are substandard grammar.
Hardly means scarcely or barely, as in almost never or almost not capable of, so to say I can hardly understand grammar rules means that for the most part, I don’t understand grammar rules. To say I can’t hardly understand grammar rules means, then, the opposite, which would be for the most part, I don’t not understand grammar rules or I cannot almost never understand grammar rules, which is not what you mean to say—and it even sounds wrong, doesn’t it?
When you use hardly, the negative is already included in that word, so you don’t need to add another negative—in this case, the can’t—in order to make it a negative. Doing so cancels the negative.
The bottom line is that when using hardly, use can hardly, not can’t hardly.
Sherry
Everything Language and Grammar 