B

设$\triangle ABD$的边$AB$上的高与$\triangle ACD$的$AC$上的高分别为$h_{1}$，$h_{2}$，
$\because AD$是$\triangle ABC$的角平分线，
$\therefore h_{1}=h_{2}$，
$S_{\triangle ABD}$：$S_{\triangle ACD}=AB:AC=6:4$，
$\because S_{\triangle ABD}$：$S_{\triangle ACD}=6:4=3:2$，
$\therefore BD:CD=3:2$.
$\because BC=8$，
$\therefore CD=\frac{16}{5}$.
故选：$B$.