The question of how many Linux distributions there are, is a very hard one to answer.
Short answer: hundreds.
Long answer: The number fluctuates based on factors such as what one considers a distribution to be, how many people have to be using (and/or aware of) it, and whether it has to be actively maintained to make the list.
Experienced Linux enthusiasts might put together their own personalized distributions, including all of the features and applications that they need, and excluding all those irrelevant to them. That counts as a distribution, right?
For the rest of us, the extent of the options available make the choice just that much more difficult.
Let’s look over 12 of the most widely-known distributions to further confuse — excuse me, I mean enlighten — the matter.