To solve this equation, we first need to consider the absolute value expressions separately.

For |x-10|, we need to look at two cases:
1) When x-10 is positive: x-10 ≥ 0 → x ≥ 10
2) When x-10 is negative: x-10 < 0 → x < 10

Similarly, for |2-x|, we also need to consider two cases:
1) When 2-x is positive: 2-x ≥ 0 → x ≤ 2
2) When 2-x is negative: 2-x < 0 → x > 2

Now, we can substitute these cases back into the original equation:

For x ≥ 10 and x ≤ 2:
3x - (x-10) - (2-x) = -6
3x - x + 10 - 2 + x = -6
3x - x + x + 10 - 2 = -6
3x = -14
x = -14/3 (Not possible because x cannot be less than 2)

For x < 10 and x > 2:
3x - (x-10) - (2-x) = -6
3x - x + 10 - 2 + x = -6
3x - x + x + 10 - 2 = -6
3x = -14
x = -14/3 (Not possible because x cannot be less than 2)

Therefore, there are no solutions to the given equation.