Player A has a Zacama, Primal Calamity, and player B has a creature with protection from green, such as Vodalian Zombie.
Player A uses Zacama's red ability deal 3 to that creature, is he able to do that? Its a red ability, but Zacama has green in it?.
Player A cannot target the creature with Zacama's ability.
It doesn't matter what the ability costs; abilities themselves do not have colors.
What matters for protection is what the source of the ability is, and the source of the ability here is Zacama, Primal Calamity. Because Zacama, Primal Calamity costs Red, Green, and White to cast, it is a Red creature, a Green creature, and a White creature. So Player B's creature has protection from Zacama, which includes all of Zacama's abilities.
First, protection from green means that that permanent can't be targeted, enchanted, dealt damage by (it is prevented) or blocked by anything that is green (see rule 702.16). Specifically with regard to targeting:
702.16b. A permanent or player with protection can't be targeted by spells with the stated quality and can't be targeted by abilities from a source with the stated quality.
So what defines a source? Glad you asked.
112.7. The source of an ability is the object that generated it. The source of an activated ability on the stack is the object whose ability was activated. The source of a triggered ability (other than a delayed triggered ability) on the stack, or one that has triggered and is waiting to be put on the stack, is the object whose ability triggered. To determine the source of a delayed triggered ability, see rules 603.7d–f.
Since Zacama, Primal Calamity's is green (and red and white), anything with protection from green (or red or white) can't be targeted by Zacama's ability or dealt damage by Zacama. So you could never even target the creature. And even if there was some way to pull that off (there isn't by the way), it wouldn't take any damage anyway.
702.16b. A permanent or player with protection can't be targeted by spells with the stated quality and can't be targeted by abilities from a source with the stated quality
This means that, even though the ability is cast using a different colour (abilities don't have colours anyway), the source of this ability contains a quality that is protected against. The card is incapable of targeting it in anyway, at all.
