[obs20]

I think I've got it.

Spoiler:

It takes 18 days.
He fills 4 bottles up and walks for 1 day towards the edge of the desert. He leaves 2 of his bottles in a safe place and walks back with one bottle for the trip back to the oasis.
He fills another four bottles at the oasis and starts again this time he travels for 1 day back to the hiding place and picks up 1 of the two bottles toward the edge and at the end of day 2 he sets 2 of his bottles at a hiding spot at the end of day 2. He travels back picking up the bottle at the day 1 spot to complete his trip back to the oasis.

He repeats the sequence above until he has 4 bottles waiting for him at the end of day 2.

Then he has the 4 bottles of water he needs to compete the 6 day trip