Hi! MathLearner. Hope ur having a great time.

ur question can easily be solved by using a small matrix

A B

00:00 00:00

00:06 11:58 after 36 hrs

01:00 11:40

02:00 11:00

one clock is goin forward and other backward even if there min hand come on same position,there hr hand won't. So using matrix for hrs we get

A B

4:00 10:00

6:00 8:00

" "

00:00 00:00

if over all time elapsed is calculated it will be a multiple of 24. Therefore if they were initially set at 12 noon they will again show same time at 12 noon after 180 days