Answer : Option C

Explanation :

Note: Assume the total work = LCM of the given time

Take the LCM of hours = LCM of (15, 12, and 4) = 60
Let the total work = 60

Note: One hour work = (total work/ time)

Now,

A's one hour work = 60/15 = 4 unit
B's one hour work = 60/12 = 5 unit
C's one hour work = 60/4= 15 unit

ATQ, between 8 am - 9 am, A works alone and finish 4 units of work
Between 9 am - 10 am, A and B work and complete 4+5 = 9 units of work
Between 10 am - 11 am, A and B work and complete 4+5 = 9 units of work
Between 11 am - 12 am, A, B works, and C destroys it. i.e., 4+5 - 9 = - 6 unit of work
Where -ve indicates destroyed work
That means after 11 am, the net work is -6 per hour.
Total work till 11 am = 4+9+9= 22 unit

Destroy 6 unit works in 1 hour, or 1 unit work in 1/6 hours.
Time taken to destroy 22 unit works = 22/6 = 11/3 hours
Or, 3[2/3] hours

Hence, at 11am + 3[2/3] hours = 2:40 pm the total work will be destroyed.