Two people can hear the sound of each other on the moon's surface. 

Sound needs something to travel through to get from one place to another. On the Moon, since there is no air, sound cannot travel above the surface. So, there are no sounds on the surface of the Moon. 
The Moon has no air because its gravity is too weak to hold an atmosphere. The gravity on the Moon is about six times less than the gravity on Earth, so any gases on the Moon (except for the very heaviest) would eventually float away into space.
Hence, the no sound can be heard on the moon's surface.