For any complex of $R$-module M, how to show that $\hom_R(f, M)$ is a quasi-isomorphism  if $f:P \to P'$ is a quasi-isomorphism of $\pi$-projective complexes of $R$-modules.

We say that a complex $P$ is $\pi$-projective, if for all quasi-isomorphisme $g: M \to M'$ 
$$\hom_R(P,g): \hom_R(P,M') \to \hom_R(P,M)$$
is a quasi-isomorphisme.

Equivalently we says that the complex of $R$-modules $P$ is $\pi$-projective, if for all exacte complex $M$, $\hom_R(P,M)$ is also exacte.

remark: $$ \hom_R(P,M) = \prod_{i \in \mathbb{Z}} \hom_R(P_i, M_{i+n})$$