[omk3]

Yes, I see now. I should have figured it out sooner.

Spoiler:

The cache at day two must be 4 or larger.
The cache can be calculated like this:
4-2x (the water we take from cache 1 minus the trip to day 2 and back, x)
+4-x (the water we take from cache 1 the second time, minus the trip to day 2)
And to get a cache of 4, x=3/4. This only works if there is 8 days' water or more in cache1.
My problem was that I wasn't sure that I would have 4 full days of water left to take from cache1 to cache2 the second time. I thought that this second load of water was unknown. In the 12 day solution, the total cache of water in day one is only 7 after all, so you only take 3 on your second trip.