Number is used with nouns that can be counted in discrete units. Amount is used with nouns that cannot be so counted.
Observe the example in the cropped image. The phrase underlined in red shows the correct use of number. Incidents do not occur in anything but whole units that can be counted discretely. Water, on the other hand, must be counted otherwise. Thus, the phrase underlined in blue shows the correct use of amount.
Using amount correctly is fairly simple, since few would actually say "the number of water." It just doesn't sound right (and that's because it isn't). However, some writers might actually say "the amount of incidents." The best way I have found to use these two words properly is simply to remember that whole numbers can be counted only discretely. That means I need to use number to reference items that can be counted in discrete units. Otherwise, amount is the word of choice.