#### Answer

$\frac{(y-12)}{(y-14)}$

#### Work Step by Step

Since the numerator and the denominator both consist of a trinomial, we use the rules of factoring trinomials in order to factor them. Then, we cancel out the resultant common factors in the numerator and the denominator:
$\frac{y^{2}-6y-72}{y^{2}-8y-84}$
=$\frac{y^{2}+6y-12y-72}{y^{2}+6y-14y-84}$
=$\frac{y(y+6)-12(y+6)}{y(y+6)-14(y+6)}$
=$\frac{(y+6)(y-12)}{(y+6)(y-14)}$
=$\frac{(y-12)}{(y-14)}$