Consider the short exact sequence of $R$-modules $$ 0 \to A \to B \xrightarrow{g} C \to 0 \,. $$ Now suppose that $C$ is a free $R$-module. Show that there is a section map $s \colon C\to B$ such that $g \circ s = \mathrm{id}_C$.
I can't come up with with $s$ explicitly so I guess I can't do that but I'm not sure. Thanks in advance.