$$2\sqrt{27} + 4\sqrt{48} - \frac{1}{5}\sqrt{75} - 9\sqrt{3} = 2\sqrt{9 \cdot 3} + 4\sqrt{16 \cdot 3} - \frac{1}{5}\sqrt{25 \cdot 3} - 9\sqrt{3} = 2 \cdot 3\sqrt{3} + 4 \cdot 4 \sqrt{3} - \frac{1}{5} \cdot 5 \sqrt{3} - 9\sqrt{3} = 6\sqrt{3} + 16\sqrt{3} - \sqrt{3} - 9\sqrt{3} = (6 + 16 - 1 - 9)\sqrt{3} = 12\sqrt{3}$$
Ответ: $$12\sqrt{3}$$