jmc

Setting $x=4$ in the given functional equation, we get $$f(4)+2f(-3)=48.$$Setting $x=-3$ in the given functional equation, we get $$f(-3)+2f(4)=27.$$Doubling the second equation, we get $2f(-3)+4f(4)=54.$ Subtracting the equation $f(4)+2f(-3)=48,$ we get $3f(4)=6,$ so $f(4)=\boxed{2}.$