Since this is an equation of absolute values, then there will either be two solutions or no solutions. To determine the solutions, we simplify algebraically first:
`2|3x-2|-6=-4` move -6 to right side
`2|3x-2|=2` divide by 2
Now there are two different equations. Find the value when the absolute value argument is negative and when it is positive.
`3x-2=-1` move to right side
Now find the positive argument solution
`3x-2=1` move to right side
There are two solutions x=1 and x=1/3, so the sum of the solutions is `1+1/3=4/3` . The graph of the solutions is: