`(3\sqrt{2}+\sqrt{6}).\sqrt{6-3\sqrt{3}}`
`=3\sqrt{2}.\sqrt{6-3\sqrt{3}}+\sqrt{6}.\sqrt{6-3\sqrt{3}}`
`=3\sqrt{2(6-3\sqrt{3})}+\sqrt{6(6-3\sqrt{3})}`
`=3\sqrt{12-6\sqrt{3}}+\sqrt{36-18\sqrt{3}}`
`=3\sqrt{(\sqrt{9}-\sqrt{3})^2}+\sqrt{(3-3\sqrt{3})^2}`
`=3|3-\sqrt{3}|+|3-3\sqrt{3}|`
`=3(3-\sqrt{3})+(3\sqrt{3}-3)` (do `3-\sqrt{3}>0;3-3\sqrt{3}<0)`
`=9-3\sqrt{3}+3\sqrt{3}-3`
`=6`