2. As shown in Figure 1, point $D$ is a point on side $B C$ of $\triangle A B C$. If $\angle C A D=$
$\angle D A B=60^{\circ}, A C$
$=3, A B=6$, then
the length of $A D$ is ( ).
(A) $\frac{3}{2}$
(B) 2
(C) $\frac{4}{3}$
(D) None of the above answers is correct
2. B.

Extend $B A$ to $E$, such that $A E=A C$. Since $\angle C 1 B=120^{\circ}$, then $\angle C A E=60^{\circ}$. Therefore, $\triangle A C E$ is an equilateral triangle. Since $C E=A C=3$, and $A D / / C E$, we have $\frac{A D}{C E}=\frac{B A}{B E}$, so $A D=\frac{3 \times 6}{9}=2$.