Factor $54=2\times 27$. Rewrite the square root of the product $\sqrt{2\times 27}$ as the product of square roots $\sqrt{2}\sqrt{27}$.
$$\frac{\sqrt{2}\sqrt{27}\sqrt{2}}{6\sqrt{12}}$$
Multiply $\sqrt{2}$ and $\sqrt{2}$ to get $2$.
$$\frac{2\sqrt{27}}{6\sqrt{12}}$$
Factor $27=3^{2}\times 3$. Rewrite the square root of the product $\sqrt{3^{2}\times 3}$ as the product of square roots $\sqrt{3^{2}}\sqrt{3}$. Take the square root of $3^{2}$.
$$\frac{2\times 3\sqrt{3}}{6\sqrt{12}}$$
Multiply $2$ and $3$ to get $6$.
$$\frac{6\sqrt{3}}{6\sqrt{12}}$$
Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.
$$\frac{6\sqrt{3}}{6\times 2\sqrt{3}}$$
Multiply $6$ and $2$ to get $12$.
$$\frac{6\sqrt{3}}{12\sqrt{3}}$$
Cancel out $6\sqrt{3}$ in both numerator and denominator.
