Interesting. I got there somewhat differently. x is the number of kids, and y the number of books

y = x * (x - 4), total number of books x kids should get, and y = (x -2) * (x - 4 + 1), two fewer kids get one more book each for the same total.

ie.

   x * (x-4) = (x-2) * (x-3)
=> x^2 - 4x = x^2 - 5x + 6
=> x = 6

Solve for y to get number of books.