Where did they get this 100-4, I realize it equals 96 but what? Can anyone explain to me why it went by 100? What am I missing here?
Because it's easier that way. That's how I figured it out in my own head before I looked at the answer in your post. I recognized from experience that 96 is a multiple of 4 (sometimes it's just a matter of practice and experience, which is why they have us memorize multiplication tables -- or at least they did when I was a kid), and when I was trying to remind myself what it factored down to, I realized, "Hey, 96 is only 4 less than 100, and I know that 100 divided by 4 is 25, so 96 divided by 4 must therefore be 24." Which was an easy way of figuring it out. (Otherwise I would've broken it down as 80 + 16, which is (20 + 4) x 4, and that would've given me the answer.)
And that meant that 25 x 96 could also be written as 25 x (4 x 24), and you just move the parentheses and it's (25 x 4) x 24 = 100 x 24 = 2400. It's just an easier and more intuitive route to the solution.
So that's two different points where it was possible to get to 100, and that made it much easier to solve those parts. We use base-10 mathematics because we have ten fingers, so anytime you can rearrange an equation to get a 10 or 100 or the like in there, it makes it easier to solve.