Let's first simplify the equation by removing the absolute value notation:

|2x - 1| + |3x + 2| = 6

From here, we can create two separate equations based on the possible signs of the expressions inside the absolute value bars:

1) When 2x - 1 is positive:
2x - 1 + 3x + 2 = 6
5x + 1 = 6
5x = 5
x = 1

2) When 2x - 1 is negative:
-(2x - 1) + -(3x + 2) = 6
-2x + 1 - 3x - 2 = 6
-5x - 1 = 6
-5x = 7
x = -7/5

Therefore, the possible solutions for the equation |2x - 1| + |3x + 2| = 6 are x = 1 and x = -7/5.