To gain immortality Hercules was tasked with twelve labors by Zeus. one of these was to clean the Augean stables in a day. The stables had never been cleaned before.
The relationship is that The Augean stables were one of the 12 tasks of Hercules. Inn the myth Hercules was tasked to clean up the Augean stables, a feat thought of as impossible.
Mythology says that Hercules was punished to carry out 12 tasks, the Twelve Labours of Hercules.
One of these tasks was to clean the Augean stables, in one day.