$\begin{align}  & \text{If }f(x)\text{ is divisible by }x-a,\text{ then }f(a)=0 \\ & \text{let }f(x)={{x}^{4}}+4{{x}^{3}}+6{{x}^{2}}-8\text{ be divided by }x+2 \\ & f(-2)={{(-2)}^{4}}+4{{(-2)}^{3}}+6{{(-2)}^{2}}-8 \\ & f(-2)=16-32+24-8=0 \\ & \text{Since }f(-2)=0,\text{ }f(x)\text{ is divisible by }x+2 \\\end{align}$