The equation |x-3|-8=20 can be solved as follows:

First, we isolate the absolute value term by adding 8 to both sides of the equation:

|x-3| = 20 + 8
|x-3| = 28

Next, we split the equation into two cases, one where the expression inside the absolute value is positive and one where it is negative.

Case 1: x - 3 is positive
In this case, the equation becomes x - 3 = 28. Solving for x, we get:
x = 28 + 3
x = 31

Case 2: x - 3 is negative
In this case, the equation becomes -(x - 3) = 28. Solving for x, we get:
-x + 3 = 28
-x = 28 - 3
-x = 25
x = -25

Therefore, the solutions to the equation |x-3|-8=20 are x = 31 and x = -25.