**4x^2+8y-4xy-8x**

I have made several attempts. Here is one of them:

4x^2+8y-4xy-8x

1) Grouped like terms together:

= (4x^2 + (-8x))+(8y + (-4xy))

2) Factored each term:

(2*2*x*x + (-1)*2*2*2*x) + (2*2*2*y + (-1)*2*2*x*y)

3) Found greatest common factor for each pair of like terms, and factored each pair by its GCF:

(4x*x+4x*(-2)) + (4y*2+4y*-x)

4) Used distributive property:

4x(x-2) + 4y(2-x)

5) Therefore, the solution to the problem is the binomial:

(4x+4y)(x-2)

However, this is wrong. The actual answer is (4x-4y)(x-2). So, I'm correct, except for the fact that 4y is positive when it should be negative.

Can someone please help understand why 4y is actually -4y?