Which direction are you facing now, if you turn $270^{\circ }$ clockwise from facing west at the beginning?

1. Initially, you are facing West ($270^{\circ }$ on the standard compass circle if North is $0^{\circ }$ /$360^{\circ }$, East is $90^{\circ }$, South is $180^{\circ }$, and West is $270^{\circ }$).
2. Turning $270^{\circ }$ clockwise means moving in the direction of North $\to$ East $\to$ South.
3. Mathematically, adding the angles:

$$270^{\circ }\text{ (Initial West)}+270^{\circ }\text{ (Clockwise turn)}=540^{\circ }$$

4. Subtract a full rotation ($360^{\circ }$):

$$540^{\circ }-360^{\circ }=180^{\circ }$$

5. A heading of $180^{\circ }$ corresponds to the South direction.