I have no idea how to go about this. Any Hint?
Suppose that $(x-3)$ is a factor of
$$kx^3 - 6x^2 + 2kx - 12.$$
Solve for $k$.
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According to the Remainder Theorem, for any polynomial $f(x)$, if $f(a)=0$, $(x-a) $ is a factor of $f(x)$.
So in your question, if $(x-3)$ is a factor, then for $a=3$, $f(x)=?$
With this fact, you can list a equation in terms of $k,x$ and also a constant("?"),where $x=a=3$.