Well, first off, let's just temporarily forget about the absolute value. All we have is 2x - 16 = 10. First we solve this.
2x-16=10
Combine like terms
2x=26
Isolate the variable through division
x=13.
Now we remember those absolute value brackets. When we have an absolute value sign, most of the time it is going to mean that we include the answer you got, and the opposite of that number as well. So in this case, x doesn't just equal 13, but it also equals -13.
x=13,-13
Hope this helped!
-TTL