Final answer:
The date wheels on an imprinter should be set to '166' for 15 June 2017, which is the 166th day of the year in the Julian calendar. The Julian calendar includes leap years every four years but accumulates a small error over time, which led to the introduction of the Gregorian calendar.
Step-by-step explanation:
The student is asking how to set the date wheels on an imprinter for 15 June 2017 using the Julian calendar date, which in this case is the 166th day of the year. The Julian calendar differs from the Gregorian calendar which is widely used today. In the Julian system, a year has 365.25 days by assuming a leap year every four years. However, this system includes a discrepancy that leads to the calendar slipping over time; a correction was made by Pope Gregory XIII introducing the Gregorian calendar, which we currently use, with a revised leap year system. When setting the date wheels on an imprinter for the Julian date, one would set it to '166' to represent the 166th day of the year. It is worth noting that the Julian calendar is currently 13 days behind the Gregorian calendar, so the Gregorian date for the 166th day of the year would not be June 15 but instead a different date.