Solution

The equations are
$$3x-y+8=0$$
$$ 6x-ky+16=0$$
Here, $$ a_{1}=3,b_{1}=-1,c_{1}=8$$
and $$ a_{2}=6,b_{2}=-k,c_{2}=16$$

The equation will represent coincident lines only when they have infinite number of solutions.

$$ \displaystyle \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$$

$$\Rightarrow \displaystyle \frac{3}{6}=\frac{-1}{-k}=\frac{8}{16} $$

Taking,
$$\displaystyle \frac{3}{6}=\frac{-1}{-k}$$

$$\Rightarrow \displaystyle \frac{1}{2}=\displaystyle \frac{1}{k}$$

$$\Rightarrow k=2 $$

Taking,
$$ \displaystyle \frac{-1}{-k}=\frac{8}{16}$$

$$\Rightarrow \displaystyle \frac{1}{k}=\frac{1}{2} $$

$$\Rightarrow k=2$$

So, the answer is $$k=2$$