Answer:
-6, -8, and 2
Explanation:
Some strategy tips: If you know your sum has to be negative, focus on the negatives first! A promising path might be to start with pairs of negatives, and try to find a third from there.
-4 + (-6) = -10; adding a positive here would get us closer to zero and further from -12, and adding -8 would overshoot it. This pair's a dead end.
-4 + (-8) = -12; we already hit our target! Adding any other number from the list would get us a different number. This one's no good either.
-6 + (-8) = -14; promising! We just need to go a little closer to zero and we'll be at -12. That distance is exactly 2, and as luck would have it, 2's on our list!
So our three numbers are -6, -8, and 2, and adding them together we find that yes, -6 + (-8) + 2 = -12!