(B) 2
For infinitely many solutions: $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$. Here, $\dfrac{3}{6} = \dfrac{-1}{-k} = \dfrac{8}{16}$, giving $\dfrac{1}{2} = \dfrac{1}{k}$, so $k = 2$.
For coincident lines (infinitely many solutions), all three ratios must be equal. Comparing $\frac{3}{6} = \frac{1}{2}$ with $\frac{-1}{-k} = \frac{1}{k}$, set $\frac{1}{k} = \frac{1}{2}$ → $k = 2$. Always check all three ratios to confirm consistency.