6. If $\triangle A B C$ has exactly one solution when $\angle A B C=60^{\circ}, A C=12, B C=$ $k$, then the range of $k$ is ( ).
(A) $k=8 \sqrt{3}$
(B) $0<k \leqslant 12$
(C) $k \geqslant 12$
(D) $0<k \leqslant 12$ or $k=8 \sqrt{3}$
6.(D).

As shown in Figure 3, according to the problem, the circle with center $C$ and radius $k$ intersects the major arc $\mathscr{A C}$ at exactly one point $B$. It is easy to see that $0<k \leqslant 12$ or $k=$ $8 \sqrt{3}$.