-14 - (2x - 8) + 4 (1/2x + 6)
We shall apply the rule of PEMDAS, and that means the addition sign will come first in the operation. So look at the second parenthesis,
4 (1/2x + 6).
The 4 multiplies everything inside the parenthesis, and that gives you
[4 * 1/2x] + 4 * 6
2x + 24
Next we go on to the first parenthesis and you now have,
(2x - 8)
(2x - 8) + 2x + 24 now becomes
2x + 2x + 24 - 8
4x + 16
Therefore, the entire expression has been reduced to
-14 - (4x + 16)
-14 - 4x - 16
Note that the minus sign just in front of the parenthesis affects both values inside the parenthesis. hence you ended up with minus times 4x, and minus times 16.
-30 - 4x
Factorize and you now have
-2 (15 + 2x)