Billy is 6
Tommy is 4 and
Bobby is 2
Proof:
I thought about this through what I think would be logical so I decided to use even numbers. If Billy is as old as Tommy and Bobby together and then 2 years later he will be twice as old as Tommy is now.
Therefore (I did a bit of guess and check) I decided Tommy must be 4 and Bobby must be 2, so Billy will be 6.
Then, 2 years later, Billy will be 8 and 8 is 2 times Tommy's age now.