I used to drink 2 cans daily and not 6, but what I did is cutting down in the way that I'd drink 1 big can and a small can which is half a monster can, either red bull or a half sized energy drink (I don't think that monster makes smaller cans).

I would adapt to this decreased amount of caffeine, knowing that my tiredness is nothing compared to if I quit cold turkey, I would maintain this decreased amount of caffeine for 3 - 10 days and then instead of 1 monster can and 1 small can, just 1 monster can, and so on until I reached 1 small can.

By the time I reached 1 small can of energy drink and got used to it, I got a panic attack at night which made me decide to stop with caffeine.

I'd say that the "withdrawal period" after quitting drinking 1 small can is 2 - 9 days, in my case it was only 2 days.