(I have answered this question about half an hour before - repeating here)
In order to show the correct time again, the clock has to be exactly 12 hours, or 12*60=720 minutes, behind. With 2 minutes per 3 hours, the clock will have to run for 3 * 720/2 = 1080 hours. 1080 hours = 45 days. The shortest interval the clock need to show the correct time is 45 days.
