Final answer:
Fafanow's original direction was West-North-West.
Step-by-step explanation:
To determine the original direction in which Fafanow was facing, we need to consider the rotations he made. He first rotated one complete revolution, which brings him back to his original direction. Then, he rotated one-eighth of a revolution, which is 45 degrees. Since he is now facing East-South-East, we need to go back 45 degrees from that direction to find his original direction.
East-South-East is the same as 22.5 degrees south of East. Therefore, his original direction is 45 degrees west of East. In compass terms, this is equivalent to West-North-West, so the correct answer is option a) West-North-West.