Equations with 2 mods

Question

I have 4 equations with mods and I need to find the params to build the function $h(x)$. Is there a method to find these?

$h(x) = ((ax + b)$ mod $c) $mod $3$

$h(0) = 0$;

$h(1) = 2$;

$h(2) = 1$;

$h(3) = 0$;

Thanks