\[3x\sqrt{9x^{2}} + \frac{4y}{{\sqrt{64y}}^{2}} =\]
\[= 3x \cdot 3|x| + \frac{4y}{8|y|} =\]
\[= 9x \cdot ( - x) + \frac{y}{2y} = - 9x^{2} + \frac{1}{2}.\]