Combining probability distributions multiplicitivly

As a simple example, let's say that I roll 2 red dice, for every dot that I get on the red dice I roll 3 green dice, so if I get a 7 on the red dice, I would roll 21 green dice. Is there a way to calculate the probability distribution P3(n) of rolling n on the green dice, if I know P1 (the probability distribution of rolling 2 red dice) and P2 ( the probability distribution of rolling 3 green dice)?

From what I understand I can generate numbers on this distribution if I generate a number, m, on the distribution P1, and then convolve P2 with it's self m times, then generate a number on that distribution. Is there an easier way?

Thanks for any help.