Algorithmics course, please explain thoroughly, I'm trying to understand.

6. (hard, 20pt) Let be a finite set of colors, and G be a directed graph on which each arc is labeled with a color in . An -walk is an infinite path v0c0v1c1v2 on G such that, for each i,G has an arc from vi to vi+1 with color ci. In particular, we say the walk starts from v0. The walk is fair if there are infinitely many prefixes of the walk on which the number of red arcs, the number of green arcs and the number of blue arcs are all the same. Prove that there is an algorithm to decide whether the graph G has a fair walk starting from a given node v0