The first mistake is that she went from 3x-2 to 3x+2. Everywhere you see "3x+2", change it to "3x-2".
Another mistake is we shouldn't use absolute value in this case. This is because we're dealing with an odd number index. In this case, the index of the root in the original equation is 3. Because there isn't any absolute value, we won't have a plus/minus.
So we should have 3x-2 = 8 for the third to last step. That solves to x = 10/3 as the only solution.