So the episode begins with Ted and Robin moving Ted's stuff in boxes.. into the moving van! Barney desperately tries to convince them no to do it.. while Marshall and Lill\y proudly proclaim how far Ted has come to this point in his life... So since no one will listen to him (Robin and Ted) then Barney "helps" but instead of coming back up for another box.. the last box in fact... he drives off with the van to use it as a hostage to blackmail ted.
Lily and Marshall end up being helpless without Ted no towels, no groceries, no microwave.. etc. So Ted and Robin end up deciding that it'd be better if eh didnt move in since both of them like their realtionship the way it was. So Ted moves back... to Lily and Marshall's happiness.