How do you split 6 gallons of water in half using 5 gallons and 4 gallons containers?

Assuming you don't use fractions of the containers:

You could fill the 5 gallon container and then decant it into the 4 gallon container until full leaving 1 gallon left in the 5 gallon container. Empty this into another container, repeat the process 2 more times and combine the 3 one gallon containers to make 3 gallons in one.