Step 1: The man starts by walking 2 km north. His facing direction is north.
Step 2: He then turns right from north — a right turn from north changes direction to east. He walks 2 km east.
Step 3: He turns right again — a right turn from east changes direction to south.
Step 4: Therefore, after the final turn, he is facing south.
The distance walked after the last turn is irrelevant for determining facing direction — the turns alone decide it.
Thus, the correct answer is $\mathbfSouth$.