SOLUTION: A person facing south takes a quarter turn to her left. She then walks 10 paces straight ahead and stops.She rotates 180 degrees and walks another 10 paces straight ahead. After

Think of this as a bird's-eye view:

She is at the red dot above, facing south (downward)

Now she's still at the red dot, but since she turned a quarter turn,
(that is, counter-clockwise, 90° to HER left, (OUR right), she's now 
facing east (OUR right).

Now she has walked 10 paces along the green line.

Now she's facing west (our left).

Now she has walked 10 paces along the same green line
and now she's right back where she started, but now she's facing 
west (our left).   

Edwin