If a 12-hour clock face reads exactly 7 o'clock, what time would the clock show 11,997 hours later?

##4" o'clock"##

##color(red)("Note that it is not stated if morning or evening!")##

The time of 7 o'clock happens every 12 hours

##11997/12=999.75 " full cycles "larr" note that the .75 is .75 of 12"##

So the clock does 999 full rotations (cycles) + a bit more

and ##0.75xx12=9## so the extra bit is 9 hours '........................................................................ Just to confirm the 9 hours remainder:

##999xx12= 11988##

So ##r=11997-11988 = 97-88 = 9 hours## ,.............................................................................

So the 7 o'clock occurs 999 times with the additional time of 9 hours

So the clock will show 7 o'clock + 9 hours = 16 hours

On a 12 hour clock the time is ##16 -12 =4" o'clock"##