已知函数 $f(x)=\left\{\begin{array}{l}-x^2-2 x, x \leq 0 \\ \left|\log _{\frac{1}{2}} x\right|, x>0\end{array}, g(x)=2[f(x)]^2-m f(x)+1\right.$, 若 $m \in(2 \sqrt{2}, 3)$, 则 $g(x)$ 零点的个数为 ( )
$\text{A.}$ 2
$\text{B.}$ 4
$\text{C.}$ 6
$\text{D.}$ 8
$\text{E.}$
$\text{F.}$