(3\sqrt2+\sqrt6)\sqrt{6-3√3}=
=\sqrt{(3\sqrt2+\sqrt6)^2 \cdot (6-3\sqrt3)}
=\sqrt{(9\cdot 2 + 6\sqrt{12}+6)(6-3\sqrt3)}
=\sqrt{(24+6\sqrt{4\cdot 3})\cdot 3(2-\sqrt3)}
=\sqrt{3\cdot (24+6\cdot 2\sqrt3)(2-\sqrt3)}
=\sqrt{3\cdot (24+12\sqrt3)(2-\sqrt3)}
=\sqrt{3\cdot 12(2+\sqrt3)(2-\sqrt3)}
=\sqrt{36[2^2-(\sqrt3)^2]}
=\sqrt{36\cdot 1}
=6