a) $6x-6y+12x^2y-12xy^2=\left(6x-6y\right)+\left(12x^2y-12xy^2\right)=6\left(x-y\right)+12xy\left(x-y\right)=\left(x-y\right)\left(6+12xy\right)=6\left(x-y\right)\left(1+2xy\right)$
b) $x^3-x+y-y^3=\left(x^3-y^3\right)-\left(x-y\right)=\left(x-y\right)\left(x^2+xy+y^2\right)-\left(x-y\right)=\left(x-y\right)\left(x^2+xy+y^2-1\right)$