Me: I need some mangoes.
My friend: Take these mangoes. There are 85.
Me: I don't need that many.
'that many' is correct? Like 'this much'/'that much', 'that easy', 'that thin'
It is important to be able to distinguish between countable and uncountable nouns. We say how many [countable noun], and how much of an [uncountable noun].
How many apples are in the refrigerator?
How much milk is in the refrigerator?
How many people attended the party?
How much wine did we drink last night?
How many bottles of wine did we drink last night?
And so on. Mangoes, like most fruit, are countable.
With countable nouns, you are correct and would say, "I don't need that many". With uncountable nouns, you would say, "I don't need that much."