Margaret, the thing to remember is that the "value" inside the absolute value can be either positive or negative, because both have the same absolute value.
With that being said, we start with the positive, so we'll change the absolute value to parentheses.
-8 + 2(4x + 6) > 20
-8 + 8x + 12 > 20
8x > 16
x > 2
Now, since 4x + 6 can also be a negative value, we can either make the whole thing negative, -4x - 6, or in this case, change the sign of the 2 we are multiplying by. Both will give the same result.
-8 - 2(4x + 6) > 20
-8 - 8x - 12 > 20
-8x > 40
x < -5 (dividing by a negative number turns the sign around)
So, anything from -5 to 2 will not make the equation true.