Puzzle ZVOM 

Workings

Hint
Start by filling the 9 gallon container, and then using that to fill the 4 gallon container.

Answer
Here are the contents of the containers after each stage:
A   B
9   0      fill A
5   4      fill B from A
5   0      empty B
1   4      fill B from A
1   0      empty B
0   1      fill B from A
9   1      fill A
6   4      fill B from A
6   0      empty B

This leaves 6 gallons in container A.