Let $M$ be an $R$-module and let $F$ be a free $R$-module of finite rank. Let $\phi : M \to F$ be an epimorphism. Then show that $M$ has a submodule $F' \cong F $ such that $M=F' \oplus \ker\phi$.
I am new to Module theory. If I apply fundamental theorem of homomorphism then $M/\ker\phi \cong F$, what to do next?