16x^3-24x^2y^2+12xy^4-2y^6
=(16x^3-2y^6)-(24x^2y^2-12xy^4)
=2(8x^3-y^6)-12xy^2(2x-y^2)
=2[(2x)^3-(y^2)^3]-12xy^2(2x-y^2)
=2(2x-y^2)(4x^2+2xy^2+y^4)-12xy^2(2x-y^2)
=2(2x-y^2)(4x^2+2xy^2+y^4-6xy^2)
=2(2x-y^2)(4x^2-4xy^2+y^4)
=2(2x-y^2)(2x-y^2)^2
=2(2x-y^2)^3