I think the wildlings will slaughter the rest of the Night's Watch after they killed Jon. Then Theon and Sansa will arrive at the Wall and Melissandre will use Theon's blood to bring Jon back to life and hail him as the new Azor Ahai. Blood of the dragon, blood of the kings of winter and Targaryen. Wielder of a dragon fired (Valyrian steel) sword which can be a true Lightbringer. Basically R'hllor's wet dream
So one of the armies will be Jon leading the remaining wildlings, possibly having been told by Sansa about what Ramsey has been up to.
I also think this season will be when Rickon reappears in the show, with a Manderley army at his back as in the books, making them one of the six.
So I would say the six armies will be:
Wildlings under Jon Snow advancing from the wall
Mormont, Hornwood and other Stark bannermen shown in the picture, meeting up with Jon having heard Sansa has left Ramsey
Manderleys with Rickon advancing from White Harbour
Arryns under Littlefinger joing with Manderleys
Boltons holding Winterfell
Freys coming to relieve the Boltons
I think it will be a battle where the first two armies meet up and lay siege, look to be gaining the upper hand, then the Freys turn up and swing the tide, but finally the Arryns and Manderleys turn up with Rickon, rally the north and kick some ass.
Then S6E10 shows the white walkers breaking through the now deserted wall as the Nights' Watch are all dead and Jon has led his army south. Dun dun duuuuunnnnnnnnnnnnnnnnnn......