Answer
This system won't have any solutions for $$k=\frac{8}{3}.$$
Work Step by Step
We need to make these two equations inconsistent by choosing the right $k$. To do this follow the steps below:
Step 1: Multiply the first equation by $3$:
\begin{align*}
3x+6y+3kz = &18\\
3x+6y+8z =& 4.
\end{align*}
If we choose $3k = 8$ i.e. $k=8/3$ then the left sides of both equations will be equal which would mean that their right sides must be equal. Since obviously $18\neq4$ this is impossible so for this particular value of $k$ the system is inconsistent i.e. it has no solutions.
