Answer
$\sqrt6+12\sqrt7$
Work Step by Step
Factor each radicand so that one of the factors is a perfect square to obtain:
\begin{align*}
&=3\sqrt{9(6)}-2\sqrt{4(6)}-\sqrt{16(6)}+4\sqrt{9(7)}\\
\end{align*}
Simplifiy each radical by taking out the square root of each perfect square factor inside the radical sign to obtain:
\begin{align*}
&=3(3)\sqrt6-2(2)\sqrt6-4\sqrt6+4(3)\sqrt7\\
&=9\sqrt6-4\sqrt6-4\sqrt6+12\sqrt7\\
&=(-94-4)\sqrt6+12\sqrt7\\
&=\sqrt6+12\sqrt7
\end{align*}
