I think, with the way that you are explaining it, you're pulling both the red strings at the same time - not thinking of it as two sided.

If you look at the red system by itself its a simple 4:1 system just that you can pull either end of it right? Just like having a system with a double block at the top and a single block with becket at the bottom right. The bit that you tie on to the becket is essentially the end that goes through the other cleat.

Now if you look at the blue system then its exactly the same - just that the ends of the rope are blocked out up at the top block. So the blue system is a 4:1 system as well.

Now because you're only pulling one end of the red system at a time its essentially tacked on to the end of the blue 4:1 system making 16:1.

simple.... ish..... I think....

cheers,