12. As shown in Figure 2, in $\triangle A B C$, $A B=6, B C=7, C A=$ $8, A D$ bisects $\angle B A C$, intersecting $B C$ at point $D, B E$ bisects $\angle A B C$, intersecting $A C$ at point $E$. If $A D$ and $B E$ intersect at point $F$, then the value of $\frac{A F}{F D}$ is ( $\quad$.
(A) $\frac{3}{2}$
(B) $\frac{5}{3}$
(C) 2
(D) $\frac{7}{3}$
(E) $\frac{5}{2}$
12. C.

By Menelaus' theorem, we have
$$
\frac{A F}{F D} \cdot \frac{D B}{B C} \cdot \frac{C E}{E A}=1 \Rightarrow \frac{A F}{F D}=\frac{B C}{D B} \cdot \frac{E A}{C E} \text {. }
$$

By the Angle Bisector Theorem, we know
$$
\begin{array}{l}
\frac{B D}{D C}=\frac{A B}{A C}, \frac{A E}{E C}=\frac{A B}{B C} \\
\Rightarrow \frac{A F}{F D}=\frac{B C}{D B} \cdot \frac{E A}{C E}=\frac{A B+A C}{A B} \cdot \frac{A B}{B C}=2 .
\end{array}
$$