$$\\\sqrt3(1+\sqrt{2})*\sqrt{6}(3-2*\sqrt{2})\\\\
=\sqrt{3*6}*[(1+\sqrt{2})(3-2\sqrt{2})]\\\\
=\sqrt{2*9}*[1(3-2\sqrt{2})+\sqrt{2}(3-2\sqrt{2})]\\\\
=3\sqrt{2}*[3-2\sqrt{2}+3\sqrt{2}-2\sqrt{2}\sqrt{2}]\\\\
=3\sqrt{2}*[3+\sqrt{2}-2*2]\\\\
=3\sqrt{2}*[\sqrt{2}-1]\\\\
=6-3\sqrt{2}$$
You need to check this answer :)
$$\\\sqrt3(1+\sqrt{2})*\sqrt{6}(3-2*\sqrt{2})\\\\
=\sqrt{3*6}*[(1+\sqrt{2})(3-2\sqrt{2})]\\\\
=\sqrt{2*9}*[1(3-2\sqrt{2})+\sqrt{2}(3-2\sqrt{2})]\\\\
=3\sqrt{2}*[3-2\sqrt{2}+3\sqrt{2}-2\sqrt{2}\sqrt{2}]\\\\
=3\sqrt{2}*[3+\sqrt{2}-2*2]\\\\
=3\sqrt{2}*[\sqrt{2}-1]\\\\
=6-3\sqrt{2}$$
You need to check this answer :)