\(=4\left(x-2y\right)-\left(x-2y\right)\left(x+2y\right)\\ =\left(x-2y\right)\left(4-x-2y\right)\)
\(4x-8y-x^2+4y^2\)
\(=-\left(x^2-4x+4\right)+4\left(y^2-2y+1\right)\)
\(=4\left(y-1\right)^2-\left(x-2\right)^2\)
\(=\left(2y-2-x+2\right)\left(2y-2+x-2\right)\)
\(=\left(2y-x\right)\left(2y+x-4\right)\)