Explanation:
each game of cribbage "binds" 4 people, each hand of chess 2 people.
15 games of cribbage means 15×4 = 60 people are playing. that leaves 0 people and therefore 0 games for chess.
2 games of chess means 2×2 = 4 people are playing.
that leaves 60-4 = 56 people for cribbage making 56/4 = 14 games of cribbage.
13 games of cribbage means 13×4 = 52 people are playing. that leaves 60-52 = 8 people for chess making 8/2 = 4 games of chess.
14 games of chess means 14×2 = 28 people are playing, that leaves 60-28 = 32 purple for cribbage making 32/4 = 8 games of cribbage.
0 people of cribbage means nobody is playing this game, that leaves all 60 people to play chess making 60/2 = 30 games of chess.