jmc

The point $(1,-2)$ is on the graph of $y=g(x)$, and the point $(-2,3)$ is on the graph of $y=f(x)$, so $$f(g(1))=f(-2)=3.$$ The point $(1,1.5)$ is on the graph of $y=f(x)$, and the point $(1.5,-1)$ is on the graph of $y=g(x)$, so $$g(f(1))=g(1.5)=-1.$$ Thus, $$f(g(1))\cdot g(f(1))=(3)(-1)=\boxed{-3}.$$