So first, you get the absolute value to one side:

Next, set up two equations; One where the value inside the absolute value lines is positive, and another where it is negative, and solve both for the variable:

Your answers are
8 and -8, or +-8.
The correct answer is ASA.
If you look at the steps given in the proof, you will see that are are given two different angles that are congruent. You also have a side that is in between the two angles. Therefore, we have ASA.