Final answer:
The correct answer is b) Apollo 13. This mission in 1970 set the record for the furthest distance humans have traveled from Earth and was known for its critical failure that led to the cancellation of the lunar landing.
Step-by-step explanation:
The farthest humans have ever been from Earth was 248,655 miles away during the Apollo 13 mission in 1970. This mission is notable for its status as a "successful failure" as the astronauts made it home safely despite an explosion on board that prevented them from landing on the Moon.
It was Apollo 8 that first rounded the Moon in 1968, and Apollo 11 marked the first Moon landing in 1969. The final manned lunar landing was with Apollo 17, ending the historical era of human lunar exploration in 1972. Although Apollo 15 is famous for its lunar rover and extensive scientific work, it did not set the record for the furthest distance from Earth - that distinction belongs to the crew of Apollo 13.