Factor $24=2^{2}\times 6$. Rewrite the square root of the product $\sqrt{2^{2}\times 6}$ as the product of square roots $\sqrt{2^{2}}\sqrt{6}$. Take the square root of $2^{2}$.
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 $3^{2}$.
$$A=4\sqrt{6}+3\sqrt{6}-2\sqrt{6}-\sqrt{155}$$
Combine $4\sqrt{6}$ and $3\sqrt{6}$ to get $7\sqrt{6}$.
$$A=7\sqrt{6}-2\sqrt{6}-\sqrt{155}$$
Combine $7\sqrt{6}$ and $-2\sqrt{6}$ to get $5\sqrt{6}$.
