They use the fact that 5! = 5* 4! and 4!= 4*3! to change 8!/(4!*4!) into 8!/(4!*(4*3!)) and 8!/(5!*3!) into 8!/((5*4!)*3!) to get 4!3! in the denominator of both quantities then factorise 8!/(4!3!)
The solution has already been given, but I thought I'd rewrite it a bit:
We have a forum that deals with how to write expressions. It's the LaTeX Help forum. It's pretty easy to learn the basics.
-Dan