Answer
$k=-4$
Work Step by Step
We have the two system of equations as follows:
$4x-8y=-3 \\ 2x+ky =16$
The system is inconsistent when it has no solution.
Thus, $\dfrac{4}{2}=\dfrac{-8}{k} \ne \dfrac{-3}{16}$
Now, $\dfrac{4}{2}=\dfrac{-8}{k} $
This implies that $k=-4$