If you start facing South-West and turn $180^{\circ }$ to your right, what direction are you facing now?

1. A turn of $180^{\circ }$ (whether to the right or to the left) always positions a person in the exact opposite direction of their initial orientation.
2. The exact opposite direction of South-West is North-East (the opposite of South is North, and the opposite of West is East).
3. Therefore, you will be facing North-East.