Answer
$\color{blue}{(y+x-6)(y-x+6)}$
Work Step by Step
Group the last three terms together to obtain:
$y^2-x^2+12x-36=y^2-(x^2-12x+36)$
The trinomial is a perfect square trinomial in the form $a^2-2ab+b^2$ with $a=x$ and $b=6$.
RECALL:
$a^2-2ab+b^2=(a-b)^2$
Use the formula above to obtain:
$=y^2-(x-6)^2$
The polynomial above is a difference of two squares.
Factor using the formula $a^2-b^2=(a+b)(a-b)$ with $a=y$ and $b=x-6$ to obtain:
$=[y+(x-6)][y-(x-6)]
\\=\color{blue}{(y+x-6)(y-x+6)}$
