Counting the difference between the clocks
Every hour, one clock goes forwards by two hours and the other goes back by one, so the difference between them grows by 3 hours. Eventually, after 8 hours, they will be 24 hours apart, or in other words they show the same time again. 8 hours after 13:00 is 21:00, at which time the clocks will both be showing 05:00.
Using algebra
After $x$ hours, the first clock will have gone forward $2x$ hours and the second clock will have gone back $x$ hours. So the next time they agree is when they have run through a total of 24 hours together, i.e. when $2x + x = 24$, that is when $x = 8$.
At 21:00 (13:00 + 8 hours) both clocks will be showing 05:00.