Sketch the region over which the joint density is defined, identify the subregion corresponding to $\displaystyle x\ge y$ then integrate the joint pdf over that region.
(note that should be:
$\displaystyle f(x,y) = \begin{cases} 12xy&,0\le x \le 1, x^2\le y\le \sqrt{x}\\0&, \text{otherwise}
\end{cases}$
as it is a joint density)
CB