See here for the original post of the puzzle.
Since Clock A is gaining 1 minute every 24 hours, and Clock B is losing 1 minute every 24 hours, then the next time they will all show noon at the same moment will be when Clocks A and B both gain/lose (respectively) 12 hours (meaning they've gotten "closer together" by 24 hours).
Since they lose/gain 1 minute every day, and there are 12 x 60 = 720 minutes in 12 hours, then it will take 720 days to reach that phenomenon.
Thus, we are looking for the date that is 720 days after January 1, 2016. Be careful because 2016 is a Leap Year! So, the final answer is December 21, 2017.