For any ring $R$ if the right regular $R$-module $R_R$ is semisimple then all right $R$-modules are semisimple.
Let $M$ be an artirary right $R$-module. In order to show that $M$ is semisimple I have considered a submodule $N \subseteq M$. I have to show that $N$ is a direct summand of $M$. On the other hand, I have a useful characterization of semisimple modules:
$M$ is semisimple iff it is the sum of a family of simple submodules.
Using these instruments how can obtain desired result