Actually, this question is hard unless you master very well the properties of exponents/roots

First off, you can NOT add two different exponent bases as you did. You can add up only when the base is the same. E.G $3^2*3^5 = 3^7$

In this case, manipulate the denominator splitting it into two factors

$\frac{2^{14} 3^{24}}{(2*3)^y} = \frac{2^{14} 3^{24}}{2^y3^y}$

As you can see for being divisible our fraction our y must contain at most 14 factors of two. Of course, the rule says that you are limited by the smallest number of factors to have a perfect division.

Hope this helps