Answer: they played 34 regular season games.
Explanation:
Let x represent the number of wins that the Phoenix Mercury had.
Let y represent the number of losses that the Phoenix Mercury had.
The Phoenix Mercury had 12 more wins than losses. It means that
x = y + 12
The number of wins they had was one more than two times the number of losses. It means that
x = 2y + 1- - - - - - - - - - -1
Substituting x = y + 12 into equation 1, it becomes
y + 12 = 2y + 1
2y - y = 12 - 1
y = 11
Substituting y = 11 into equation 1, it becomes
x = 2 × 11 + 1
x = 22 + 1
x = 23
Therefore, the total regular season games that the Phoenix Mercury played during that season is
23 + 11 = 34