Factor $54=3^{2}\times 6$. Rewrite the square root of the product $\sqrt{3^{2}\times 6}$ as the product of square roots $\sqrt{3^{2}}\sqrt{6}$. Take the square root of $3^{2}$.
Combine $6\sqrt{6}$ and $4\sqrt{6}$ to get $10\sqrt{6}$.
$$\frac{10\sqrt{6}}{4\sqrt{8}-3\sqrt{2}}$$
Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.
