Harold's house is 12 km from the shopping center. His school is on the same road. If Harold travels from home to school and back, he travels half the distance from home to the shopping center. What is the distance from his school to the shopping center?

If Harold travels half the distance from home to the shopping center, then the distance from his school to the shopping center is 12 km / 2 = <<12/2=6>>6 km. Answer: \boxed{6}.