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.

unboiled

I initially tried to build two equations with two unknowns, $$b$$ and $$c$$, but they didn't come out linear, so rather than mess with more algebra I resorted to guess and check instead.

SimpleStacker

science

Secondary school math puzzle

Scroogey

There is a way without trying, but building the equation was the tricky part (solving it is simple).

Let's define $$x$$ as the number of children.
Every child should get $$x-4$$ books, and there are $$x \times (x-4)$$ books.
The number of books freed by the 2 children who don't like them is $$2 \times (x-4)$$.
That's the same number as are given to the remaining children i.e. $$(x-2) \times 1$$.
Hence, $$2 \times (x-4) = (x-2) \times 1$$ or $$x = 6$$.