How to prove that for $K$ $\mathbb{Z}$-free & $Q$ projective, $K\otimes_{\mathbb{Z}}Q$ is a projective?

Question

Let $K$ be $\mathbb{Z}$-free and $Q$ a projective $\mathbb{Z}G$ module then $K\otimes_{\mathbb{Z}}Q$ is a projective $\mathbb{Z}G$-module. I believe that this follows from the adjoint isomorphism theorem:

$Hom_{\mathbb{Z}G}(K\otimes Q, N)=Hom_{\mathbb{Z}}(K,Hom_{\mathbb{Z}G}(Q,N))$

But I don't understand why? Any ideas would be helpful, I just don't know where to start.