algebra

Factor out$8m^2+16m$ to get$8m(m+2)$.

Factor out$m^2-m-6$ to get$(m+2)(m-3)$.

Factor out$4m^3+8m^2$ to get$4m^2(m+2)$.

$\frac{8m(m+2)}{m-3}\times\frac{(m+2)(m-3)}{4m^2(m+2)}$.

"Crossing off" $4m(m+2)$ we get $\frac{2}{m-3}\times\frac{(m+2)(m-3)}{m}$

"Crossing off" $m-3$ we get $2\times\frac{m+2}{m}$

Solving, we get $\frac{2m+4}{m}$.

You are very welcome!
:P