If the bowls have measuring marks then we don't need to do anything gexcept fill the 9 liter container up to where is says 6 liters. About the post that mentions not pouring the water on the floor, why would it suddenly become unusable? He never said it was going onto the floor, he could have anouther caontainer that he can pour it into. But, since he doesn't know the container's volume, he can't use it fore measuring. In cooking, can't you measure some of the water at a time if you need a lot and put that measured water into a bowl of unknown volume?
No, another vessel is prohibited by the language of the question "using only a 4 liter bowl and a 9 liter bowl."
However, there is a deeper problem with this proposed solution, I'm surprised no one else has picked up on...
What about filling up 4 liter, 6 times, and every time pouring it into the 9 liter?
That way 6 liters will spill out.
Correct me if I'm misunderstanding something, but (4x6)-9=15. So you've correctly "measured" 15 liters onto the floor, not 6. To get 6 liters to spill you must put three volumes of 4 liters into the 9, then empty the 9, rinse and repeat, but how do you distinguish between the 6 you are spilling on purpose and the 9 you are dumping out of necessity?