12. As shown in the figure, points $A(m, 8), B(n, 2)$ lie on the graph of the inverse proportion function $y=\frac{k}{x}$, $A D \perp x$-axis at point $D$, $B C \perp x$-axis at point $C$, and $D C=6$. Then $k=$ $\qquad$
$16$