Puzzle ZBOE 

Workings

Hint
Start by filling the 11 gallon container.

Answer
Here are the contents of the containers after each stage:
A  B
0  11  fill B
7  4   fill A from B
0  4   empty A
4  0   fill A from B
4  11  fill B
7  8   fill A from B
0  8   empty A
7  1   fill A from B
0  1   empty A
1  0   fill A from B
1  11  fill B
7  5   fill A from B
0  5   empty A
5  0   fill A from B
5  11  fill B
7  9   fill A from B
0  9   empty A

This leaves 9 gallons in container B.