The key to this question is to choose a number that you can use to denote the total amount of work.

I'm going with 18 since that is the highest number that in the answers and is divisible by 6,2,and 3

So there are 18 total units of work

Tom can finish 18 units in 6 hrs.. So he works at a rate of 3 units/hr

Peter finishes in 3 hrs .. = 6 units/hr

John finishes in 2 hrs = 9 units/hr

Now let's go on an hour by hour basis.

Hr 1 | 3 units of work done (Tom works alone)
Hr 2 | 3 + 6 units of work done (Tom + Peter)

Now at the end of hr 2 we have 12 units of work done in total.

18-12 = 6 units of work...

6 units of work will be distributed among Tom, Peter and John.

If you compare their rates of work.

T:P:J = 3:6:9 ... Peter will do 6/18th or 1/3 of the remaining 6 units = 2 units

Total work that Peter does = 6 (from hr 2) + 2 (from hr 3) = 8

So peter does 8 units out of 18 ... = 8/18 = 4/9

This is an easy problem if you choose the right number... Otherwise you will spend ages trying to figure out the answer!