You may want to review equations with one absolute value first.
If there are two absolute values in an equation, then it's harder. We'll just deal with the case where the equation is just two absolute values being set equal to each other. For example, the problem might be |−2x − 1| = |−2x + 1|. For two absolute values to be equal, either the things on the inside have to be equal, or else they have to be additive inverses of each other. So we have to solve two equations. The first one, −2x − 1 = −2x + 1, has no solution. The second one, −2x − 1 = 2x − 1, has solution 0. So 0 is the solution. If both equations had solutions, then they would both be solutions to the given equation, and you'd have to write both of them to get full credit.