The days mission was to coach a friend of mine through his three bangs-and-goes using another friends Cessna 172. Although he had little time, if any, in Cessnas, he was in the left seat. I was serving as PIC from the right. Shortly after we secured the cabin and ran the before-start checklist, the mighty 160-hp Lycoming was happily purring away. We were getting ready to call for a taxi clearance when the engine stopped. No cough, no protest, no warning. What did you do? I asked. Nothing, the bang-and-go candidate responded. So we ran the checklist again. When we came to the floor-mounted fuel selector, I asked, How did the fuel selector get turned off? He said, Its not; I turned it to both before starting the engine and havent touched it since. Houston, we found the problem.