To find the sum of the roots of the equation |2x-3| = 4, we first need to solve for x.

When |2x-3| = 4, we have two possible equations:

Solving the first equation:
2x - 3 = 4
2x = 7
x = 7/2

Solving the second equation:
-(2x - 3) = 4
-2x + 3 = 4
-2x = 1
x = -1/2

Therefore, the two roots are x = 7/2 and x = -1/2.

The sum of the roots is (7/2) + (-1/2) = 6/2 = 3.

Therefore, the sum of the roots of the equation |2x-3| = 4 is 3.