Answer
$3x^{2}y^{2}(x-1)(x+1)$
Work Step by Step
$ 3x^{4}y^{2}-3x^{2}y^{2}\qquad$... factor out the common term, $3x^{2}y^{2}$
$=3x^{2}y^{2}(x^{2}-1)\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=3x^{2}y^{2}(x-1)(x+1)$