Which way are you facing now, if you spin $270\text{ degrees}$ clockwise from North at the beginning?

Initially, you are facing North ($0^{\circ }$ or $360^{\circ }$).
Spinning $270^{\circ }$ clockwise from North shifts your direction through the following quadrants:

* $90^{\circ }$ clockwise $\to$ East
* $180^{\circ }$ clockwise $\to$ South
* $270^{\circ }$ clockwise $\to$ West

Alternatively, a $270^{\circ }$ clockwise rotation is equivalent to a $90^{\circ }$ counter-clockwise rotation ($360^{\circ }-270^{\circ }=90^{\circ }$). Moving $90^{\circ }$ counter-clockwise from North directly points to West.