\[\begin{array}{l}
a)2\sqrt 3 - 3\sqrt {12} + \frac{1}{5}\sqrt {75} - \frac{5}{6}\sqrt {108} \\
= 2\sqrt 3 - 3.2\sqrt 3 + \frac{1}{5}.5\sqrt 3 - \frac{5}{6}.6\sqrt 3 \\
= 2\sqrt 3 - 6\sqrt 3 + \sqrt 3 - 5\sqrt 3 \\
= - 8\sqrt 3 \\
b)(\sqrt {12} + 2\sqrt {27} - 3\sqrt 3 )\sqrt 3 \\
= (2\sqrt 3 + 2.3\sqrt 3 - 3\sqrt 3 )\sqrt 3 \\
= 5\sqrt 3 .\sqrt 3 \\
= 15\\
c)\frac{2}{{3\sqrt 2 - 4}} - \frac{2}{{3\sqrt 2 + 4}}\\
= \frac{{2(3\sqrt 2 + 4)}}{{18 - 16}} - \frac{{2(3\sqrt 2 - 4)}}{{18 - 16}}\\
= 3\sqrt 2 + 4 - 3\sqrt 2 + 4\\
= 8\\
d)\sqrt {{{(2 + \sqrt 3 )}^2}} + \sqrt {{{(\sqrt 3 - 3)}^2}} \\
= |2 + \sqrt 3 | + |\sqrt 3 - 3|\\
= 2 + \sqrt 3 + 3 - \sqrt 3 (do:2 + \sqrt 3 > 0;\sqrt 3 - 3 < 0)\\
= 5\\
e)\sqrt {{{(4 - \sqrt {11} )}^2}} + \sqrt {{{(4 + \sqrt {11} )}^2}} \\
= |4 - \sqrt {11} | + |4 + \sqrt {11} |\\
= 4 - \sqrt {11} + 4 + \sqrt {11} (do:4 - \sqrt {11} > 0;4 + \sqrt {11} > 0)\\
= 8\\
f)\sqrt {29 - 12\sqrt 5 } \\
= \sqrt {20 - 2.2\sqrt 5 .3 + 9} \\
= \sqrt {{{(2\sqrt 5 - 3)}^2}} \\
= |2\sqrt 5 - 3|\\
= 2\sqrt 5 - 3(do:2\sqrt 5 - 3 > 0)\\
g)\sqrt {4 + \sqrt 7 } + \sqrt {4 - \sqrt 7 } \\
= \frac{{\sqrt {8 + 2\sqrt 7 } + \sqrt {8 - 2\sqrt 7 } }}{{\sqrt 2 }}\\
= \frac{{\sqrt {7 + 2\sqrt 7 + 1} + \sqrt {7 - 2\sqrt 7 + 1} }}{{\sqrt 2 }}\\
= \frac{{\sqrt {{{(\sqrt 7 + 1)}^2}} + \sqrt {{{(\sqrt 7 - 1)}^2}} }}{{\sqrt 2 }}\\
= \frac{{|\sqrt 7 + 1| + |\sqrt 7 - 1|}}{{\sqrt 2 }}\\
= \frac{{\sqrt 7 + 1 + \sqrt 7 - 1}}{{\sqrt 2 }}(do:\sqrt 7 + 1 > 0;\sqrt 7 - 1 > 0)\\
= \frac{{2\sqrt 7 }}{{\sqrt 2 }}\\
= \sqrt 2 .\sqrt 7 = \sqrt {14} \\
h)\sqrt {7 - 2\sqrt {10} } + \sqrt {7 + 2\sqrt {10} } \\
= \sqrt {5 - 2\sqrt {10} + 2} + \sqrt {5 + 2\sqrt {10} + 2} \\
= \sqrt {{{(\sqrt 5 - \sqrt 2 )}^2}} + \sqrt {{{(\sqrt 5 + \sqrt 2 )}^2}} \\
= |\sqrt 5 - \sqrt 2 | + |\sqrt 5 + \sqrt 2 |\\
= \sqrt 5 - \sqrt 2 + \sqrt 5 + \sqrt 2 (do:\sqrt 5 - \sqrt 2 > 0;\sqrt 5 + \sqrt 2 > 0)\\
= 2\sqrt 5
\end{array}\]