Josh is a janitor in a hospital. Derek is a doctor in the same hospital.
When Brian complains about being fired from Parent Boppers for his changes in "Brian's a Bad Father", he claims it is like firing a doctor in the middle of an operation. A cutaway shows Josh finding a patient whose doctor suddenly disappeared and decides to make the most of the opportunity to perform the operation himself. Derek passes by and sees Josh's abandoned mop bucket and decides to use the opportunity to perform janitorial work.