Given:
1 > g > 1/2
-1 < h < -1/2

IMPORTANT
If we have two different inequalities in which the inequality signs are facing the same direction, then we can ADD the inequalities to get a new, valid inequality.
However, we can't SUBTRACT them (for more on this, watch: https://www.gmatprepnow.com/module/gmat ... /video/982)

That said, we can still use the above ADDITION strategy once we do one thing first
Take -1 < h < -1/2 and multiply all 3 parts by -1
Since we're multiplying by a NEGATIVE value, we must REVERSE the inequality signs to get: 1 > -h > 1/2

We now have:
1 > g > 1/2
1 > -h > 1/2

Since the inequality signs are facing the same direction, we can ADD the inequalities to get: 1 + 1 > g + (-h) > 1/2 + 1/2
Simplify to get: 2 > g - h > 1
We can also write this as 1 < g - h < 2

Answer: E