To solve the equation, we need to consider different cases based on the signs of the absolute values.

Case 1: x - 3 ≥ 0 and 3x - 6 ≥ 0
In this case, both absolute values are positive, so we can remove the absolute value signs.
x - 3 + 3x - 6 - (5 - 2x) = 8
Combine like terms:
4x - 4 = 8
Add 4 to both sides:
4x = 12
Divide both sides by 4:
x = 3

Case 2: x - 3 ≥ 0 and 3x - 6 < 0
In this case, the first absolute value is positive, but the second is negative, so we need to negate the second absolute value.
x - 3 + 3x - 6 + (5 - 2x) = 8
Combine like terms:
2x - 4 = 8
Add 4 to both sides:
2x = 12
Divide both sides by 2:
x = 6

Case 3: x - 3 < 0 and 3x - 6 ≥ 0
In this case, the first absolute value is negative, but the second is positive, so we need to negate the first absolute value.
-(x - 3) + 3x - 6 - (5 - 2x) = 8
Distribute the negative sign:
- x + 3 + 3x - 6 - (5 - 2x) = 8
Combine like terms:
2x - 8 = 8
Add 8 to both sides:
2x = 16
Divide both sides by 2:
x = 8

Case 4: x - 3 < 0 and 3x - 6 < 0
In this case, both absolute values are negative, so we need to negate both absolute values.
-(x - 3) + 3x - 6 + (5 - 2x) = 8
Distribute the negative signs:
- x + 3 + 3x - 6 + 5 - 2x = 8
Combine like terms:
x + 2 = 8
Subtract 2 from both sides:
x = 6

Therefore, the solutions to the equation |x-3|+|3x-6|-|5-2x|=8 are x = 3, x = 6, and x = 8.