3. A line with an inclination angle of $60^{\circ}$ is drawn through the focus $F$ of the parabola $y^{2}=8(x+2)$. If this line intersects the parabola at points $A$ and $B$, and the perpendicular bisector of chord $A B$ intersects the $x$-axis at point $P$, then the length of segment $P F$ is
A. $\frac{16}{3}$
B. $\frac{8}{3}$
C. $\frac{16 \sqrt{3}}{3}$
D. $8 \sqrt{3}$
Solve
$\frac{p}{2}=2 \Rightarrow F(0,0)$. Combine the equations $\left\{\begin{array}{l}y^{2}=8(x+2), \\ y=\sqrt{3} x\end{array}\right.$
$$
\Rightarrow 3 x^{2}-8 x-16=0 \Rightarrow M\left(\frac{4}{3}, \frac{4 \sqrt{3}}{3}\right) \text {. }
$$

Thus $|M F|=\frac{8}{3} \Rightarrow|P F|=2|M F|=\frac{16}{3}$.
Therefore, the answer is $A$.