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 $2^{2}$.
$$\frac{21\times 2\sqrt{3}}{10\sqrt{27}}$$
Multiply $21$ and $2$ to get $42$.
$$\frac{42\sqrt{3}}{10\sqrt{27}}$$
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 $3^{2}$.
$$\frac{42\sqrt{3}}{10\times 3\sqrt{3}}$$
Multiply $10$ and $3$ to get $30$.
$$\frac{42\sqrt{3}}{30\sqrt{3}}$$
Cancel out $6\sqrt{3}$ in both numerator and denominator.
