Factor

6x^2-6y^2
6(x+y(x-y) or 6(x-y)^2 ??

factor out the 6

6(x^2 - y^2)

Now you have the difference of two squares, so we end up with

6(x+y)(x-y)

Note: (x-y)^2 = x^2 - 2xy + y^2
Not what we have here