\[6\sqrt{3} + \sqrt{27} - 3\sqrt{75} =\]
\[= 6\sqrt{3} + \sqrt{9 \cdot 3} - 3\sqrt{25 \cdot 3} =\]
\[= 6\sqrt{3} + 3\sqrt{3} - 15\sqrt{3} = - 6\sqrt{3}.\]