The roots of the equation $|x^2-x-6|=x+2$ are 

The given equation is $|x^2-x-6|=x+2$

The above equation can be written as 

$\begin{array}{rcl}{x}^2-x-6& =& x+2\\ x^2-2x-8& =& 0\\ x^2-4x+2x-8& =& 0\\ x\left(x-4\right)+2\left(x-4\right)& =& 0\\ \left(x+2\right)\left(x-4\right)& =& 0\end{array}$

It implies that $x=4,-2$

Suppose that 

$\begin{array}{rcl}{x}^2-x-6& =& -x-2\\ x^2& =& 4\\ x& =& \pm 2\end{array}$

Therefore, the roots of the given equation are $\boxed{\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{4}}$