3. In $\triangle A B C$, $\angle B=2 \angle C, A C=6$. Then the range of $A B$ is ( ).
(A) $A B>3$
(B) $3<A B<6$
(C) $3 \leqslant A B<6$
(D) None of the above
3. B.

As shown in Figure 5, extend $C B$ to point $D$ such that $B D = A B$, and connect $A D$. Then,
$$
\begin{array}{c}
\angle D = \angle B A D . \\
\text { Therefore, } \angle C \\
= \frac{1}{2} \angle A B C = \angle D .
\end{array}
$$

Thus, $A D = A C = 6$.
In $\triangle A B D$, since $A B + B D > A D$, we have,
$$
2 A B > 6 \Rightarrow A B > 3 \text {. }
$$

In $\triangle A B C$, since $\angle C < \angle A B C$, we have, $A B < A C = 6$.
Therefore, $3 < A B < 6$.