I found this problem on a French exchange forum :
Find all the $f : \mathbb{R} \to \mathbb{R}$ satisfying $f(f(x)+3y)=12x + f(f(y)-x)$
In fact I solved the problem when $f$ is supposed to be continuous. Then it can be shown that $f(x)=3x+\lambda$ for some real constant $\lambda$.
What about the general case, when we do not suppose $f$ to be continuous?