how do i solve an equation like this |x+2| >(with a line underneath the >) 8

It took me a while to work that one out lol

$$|x+2|\ge 8$$

This says "The absolute value of (x+2) is greater than or equal to 8.

This means that x+2 must be further from zero (or equal to) on the number line than 8 as shown on this number line.

So 

$$\begin {array}{rlllrll}
x+2 &\le& -8\qquad &or& \qquad x+2&\ge& 8 \\
x+2-2 &\le& -8-2\qquad &or& \qquad x+2-2&\ge& 8-2\\
x &\le& -10\qquad &or& \quad \qquad x&\ge& 6\qquad
\end{array}$$