Here's the problem: Find sets $\displaystyle A, B$ and $\displaystyle C$ and functions $\displaystyle f:A\longrightarrow B, g:B\longrightarrow C$ and $\displaystyle h:B\longrightarrow C$ for which $\displaystyle f\circ h=f\circ g$ but $\displaystyle g\not=h$.

It doesn't even have to be real example functions, just a picture would be good. I just can't think of anything. Thank you!