I dont think this is possible,if he wrote for exactly four hours.

When he starts,the short hand has to be between 2 and 3,and when he finishes,it has to be between 6 and 7.

Since the hands are interchanged,the long hand has to be initially between 6 and 7,and end up between 2 and 3.

But since he wrote exacty for 4 hours,the long hand should come back to its exact minute after the 4 hrs.

well, I guess the ques should have said about 4 hours!!! then we may have a solution!

Case 1:

if the hour hand is between 2 and 3... and the minute hand b/w 6 and 7,

then the hour hand should be between 2nd and 3rd div between 2 and 3!......(1)

Case 2:

if the hour hand is between 6 and 7... and the minute hand b/w 2 and 3,

then the hour hand should be between 1st and 2nd div between 6 and 7!......(2)

that gives us an approx start time of 2:31 PM and finish at 6:12 PM

PS: forget brainstorming for a while...just get two clocks and play...u'll get the soln straightaway!!! ;)