"Quanto" and "quanta" are singular and used in phrases where who speaks is referring to uncountable nouns, and so translated in "much".
"Quanti" and "Quante" are plural and used in phrases where who speaks is referring to countable nouns, and so translated in "many".
What about this:
"Quanta gente c'era alla festa?" since "quanta" is singular, who is speaking is not specifically asking for the actual number of people. Nonetheless, "gente"="people" and "people" is a countable noun, the correct translation is "How many people were at the party?".
The same translation goes for "Quante persone c'erano alla festa?", but in this case, since "quante" is plural, who is speaking wants to know the actual number of people. So, two meanings, one translation... how can one tell the difference? No idea! :D Maybe the first question can be translated in a different way?
It is English that determines whether you will translate as "how many" or "how much".
Italian uses quanto/quanta/quanti/ quante and these must agree in gender and number with the noun. It doesn't distinguish as English does between "much" and "many".
If the noun is uncountable (e.g.water/salt/ air) in English use "how much" Quanto zucchero vuole? = How much sugar does he want? If the noun is countable then in English we use "how many". Quanti cavalli vuole? = How many horses does he want?
Mukkapazza, great answer, as always, but I think most people will find it clearer to understand that 'quanto' (or quanta) generally means 'how much'... e.g. quanto costa (how much is it (singular)) or 'quanto costano' (how much are they (plural)) whereas Quanti (and quante) always mean 'how many.'
of course 'quanta gente' is one of those oddities, which we think of as plural (as in 'the people are' (not 'the people is') whereas I believe it is thought of as singular, in Italian. Please correct me if I'm wrong!
Several previous comments are about quanto etc. as an adjective when agreement with gender and number is essential. This question was in a section about adverbs. When quanto is used as an adverb it does not change to agree with anything. Both "how many" and "how much" are correct translations since we have no context. Just saying.
Any body else getting an error with Si.?? Twice in the past few sentences, I've written them correct. ex: This one I wrote, Si, ma quanto? Each time it says... Almost Correct! And it highlights the Si. Why? I've spelled it right, it's been the 1st word, and I even capitalized the Beginning of it. So Why mark it as ... Not quite right?
Quanto and quanta are both acceptable because in this sentence we don't know the context. In a real life conversation you would know what they are asking "how much?" about and use quanto if it's a masculine noun and quanta if it's a feminine noun.
Ie. "Io voglio del riso" "Sì, ma quanto?" (quanto because the second person is still talking about "il riso")