its hard to give a useful hint that isn't the answer itself. Try thinking along these lines:

Suppose i took out 2 discs, it it possible that no 3 of them are the same color?

Yes, (obviously since there aren't 3 discs!). eg 2 could be blue, none yellow.

Suppose i took out 3 discs, it it possible that no 3 of them are the same color?

Yes, eg 2 could be blue, one yellow (or the other way around)

Keep going until you find that it is impossible (it wont take long!)