It took me a while to work out a solution. Oddly enough, my method wasn't exactly "correct"... I always came up with half the correct number and had to arbitrarily multiply by two. A bit of reading online showed that I was working along the right lines, though. (It also explained why sixes bollixed my orderly explanation.)
But it seems this game has a history of challenging people to invent creative solutions.
If you've never seen it before, I'd urge you to try it. I will say that there is a simple algorithm for determining the answer which can (demonstrably) be arrived at in a number of ways. There isn't any gimmick involving the players; it's all on the dice.
1. The name of the game is Petals Around the Rose. This is significant.
2. The answer will always be a positive even number or zero.
3. You cannot reveal the algorithm you use, only the numerical answers.
Note that rule three applies to any comments on this entry! :)
My Broken Solution:
If you already know the correct answer, you might try to deduce what I did wrong. My initial answers were off by 2 (4 after doubling) for every six rolled. I was interpreting the word "rose" incorrectly, as it turns out.