1 minute 12 seconds is 1.2 minutes (12 seconds being one fifth of a minute). The clock only registers 58 minutes and 48 seconds for every hour that passes, hence divlong's 58.8 minutes.
The way I did it is this. The clock loses 6 minutes every 5 hours, so in 15 hours it loses 18 minutes. Add another 4 minutes 48 seconds (to bring the time up to 19:00 hours) and the clock has lost 22 minutes 48 seconds by 19:00.
The clock loses 1.2 seconds per minute, so 46 x 1.2 = 55.2 seconds. Add that to the 22 minutes 48 seconds it has already lost and by 19:46 on the clock it is 23 minutes 43 seconds slow (to the nearest second).
!9:46 + 0:23:43 = 20:09 and 43 seconds as Azalian said originally.
There are other ways to get there - (number of minutes elapsed x loss per minute)/60 will give you the total time lost which you then add on to the time shown on the clock is one, divlong's method is another.