With the death of Arthur Minit, the legendary country of MADADIA's only clock maker, no one else had much experience yet with making clocks. The new church of MADADIA had just been completed and a new clock was needed to fit into the bell tower. A clock was made by the locals, using the books of Arthur Minit as a guide.The newly made clock was officially put into use when it showed 6 o'clock. But soon it was noticed that the hour-hand and minute-hand had been interchanged and attached to the wrong spindles. The result was that the hour-hand moved with a speed twelve times higher than the minute-hand. When a clock maker arrived from another area, a remarkable thing happened: on the moment he inspected the clock, it showed exactly the right time.

The Question: If the clock started in the 6 o'clock position, then what was the first moment that it showed the correct time again?