The correct way would be "How much homework". You would use "how many" if it was more than one collection of something. For example, "how much money do you have in your bank account?" You could also ask, "How many dollars are in your bank account?"
How much homework. Use many if you are indicating something that is an actual plural, not a collective plural or unquantifiable amount: how much homework did you get over how many days? Is a correct question.