Probably about 7 quarts.
FWIW, Honda's weird about people doing anything other than 3-4 drain and refills (with short drives in-between) when attempting to do a complete "flush." I think their intent was to stop folks from using BG/MOC flush machines that require the usage of snake oil additives with a transmission service.
Nowadays I just do a cooler line flush on Hondas like any other car. Drain 3 quarts, add 3. Start car, let 3 come out. Repeat once more. Add enough fluid until the level hits the minimum mark (usually 2.5 qt at this point). Idle car until radiator fans come on twice. Adjust level accordingly. I usually go thru 9 quarts with this procedure and my results are much better than the quadruple drain-and-refill method.