how to solve sqrt3(x+2) -6=-2

I am not sure what you really meant but;

$$\begin{array}{rll}
\sqrt3(x+2)-6&=&-2\\\\
\sqrt3(x+2)&=&4\\\\
x+2&=&\dfrac{4}{\sqrt3}\\\\
x+2&=&\dfrac{4\sqrt3}{3}\\\\
x&=&\dfrac{4\sqrt3}{3}-2\\\\
x&=&\dfrac{4\sqrt3-6}{3}\\\\
\end{array}$$