Final answer:
After canceling out the north and south movements, Joe is 2 miles west of his starting position. No changes occurred in the north-south direction as those displacements canceled each other, leaving the net movement only in the west direction.
Step-by-step explanation:
To determine how far Joe is from his starting position and in what direction, we can visualize his movement as a series of vector displacements. First, Joe goes 2 miles north, then 2 miles east, subsequently 2 miles south, and finally 4 miles west. After going north and then south by the same distance, these two movements cancel each other out. Joe's east and west movements, however, do not cancel each other out completely, as he moves 2 miles to the east and 4 miles to the west.
This results in Joe being 2 miles west of his starting position, with no change in the north-south position because those movements canceled each other out. Hence, the correct answer is B. 2 miles west.