elementary number theory - If $d$ divides $k$ and $d$ divides $n$, then $d$ divides $(8k - 3n)$

Suppose that $k$, $n$, and $d$ are integers and $d$ is not $0$. Prove: If $d$ divides $k$ and $d$ divides $n$, then $d$ divides $(8k - 3n)$. You may not use the theorem stating the following:

Let $m$, $n$, and $d$ be integers.

(a) If $d\mid m$ and $d\mid n$, then $d\mid (m + n)$.

(b) If $d\mid m$ and $d\mid n$, then $d\mid (m - n)$.

(c) If $d\mid m$, then $d\mid mn$.

I am not sure what the basis step is with this proof. Thank you for any help.