It's a simple question of countable and uncountable nouns. The number of people The number of children The number of books These are all countable nouns, in the plural, so we use number. One, two, three. We count them. One, two, three = numbers. The amount of time. The amount of effort. The amount of water. These are all uncountable nouns, in the singular. We can quantify these things, but we can't actually count them. Look at these two examples: I can't believe the amount of time I've spent on this essay. I can't believe the number of times I've asked this question. This uses 'time' with two different meanings - the amount of time (on the clock) and the number of times (separate occasions). I hope this makes it clearer for you.

Number of beers refers to how many bottles or if you ordered it in glasses it refers to haw many glasses of beer. The amount of beer refers to the total volume of beer (adding up the volume of all the bottles/glasses that a person drank, into one number). It could refer even to a small amount, like half a glass. By the way, I don't recommend to drink a lot of beer. But this above is just to answer the question.

I agree with Lydia. I can't believe the number of beers I drank. (I drank 12 beers) I can't believe the amount of beer I drank. (I drank A LOT of beer) Notice also what happens to "beer" with the two words. With "number", "beer" is countable. With "amount", "beer" is uncountable.