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