If you start facing East and turn $270^{\circ }$ anticlockwise, what direction are you facing now?

Let's visualize the cardinal directions: North is upwards, East is to the right, South is downwards, and West is to the left.
1. Initially, you are facing East.
2. Turning $270^{\circ }$ anticlockwise (counter-clockwise) is equivalent to:
* A $90^{\circ }$ anticlockwise turn brings you facing North.
* Another $90^{\circ }$ ($180^{\circ }$ total) brings you facing West.
* Another $90^{\circ }$ ($270^{\circ }$ total) brings you facing South.

Alternatively, a $270^{\circ }$ anticlockwise turn is equivalent to a $360^{\circ }-270^{\circ }=90^{\circ }$ clockwise turn. Turning $90^{\circ }$ clockwise from East points directly to the South.