The level 6 dark barracks needs 9 days. Prior to the lava hound update, all updates (including building and lab) that take more than 7 days, take an even number of days (8,10,12,14).
But why did the level 6 dark barracks break this tradition? Since the dark barracks is planned to have 10 levels in total, and SC doesn't want an upgrade to take more than 14 days, the upgrade times need to be scaled in some way. The plan is probably level 6 - 9 days, level 7 - 10days, level 8 - 11 days, level 9 - 12 days, and level 10 - 13 or 14 days.
However, the level 7 dark barracks take 12 days, which leads to two questions:
1. if they really want the level 7 dark barracks take 12 days, why didn't let the level 6 dark barracks take 10 days?
2. if level 7 dark barracks take 12 days, how many days should the future level 8, 9 and 10 dark barracks take?
And loot at the costs, the differences are 500000, 500000, 500000, 500000, 750000 and 2500000 respectively.
Maybe, in fact, 6000000 elixir and 12 days was originally intended to be level 8 or 9 dark barracks' cost and time.