Which direction are you facing now, if you walk $10\text{ meters}$ to the North and then turn $180^{\circ }$ to the right?

1. Initially, walking $10\text{ meters}$ to the North means you are facing the North direction.
2. Turning $180^{\circ }$ (either clockwise/right or counter-clockwise/left) completely reverses your facing direction.
3. The opposite direction of North is South.

Therefore, you are facing South now.