After last week's recap, normal (well, as normal as this show gets) service is resumed with the beginnings of a new story arc, that being Kabukimonogatari and a returning focus upon Mayoi Hachikuji. Firstly however, we learn that Araragi really doesn't know a whole lot about how traffic lights work courtesy of Ougi Oshino (who I don't believe we've been introduced to before).
Actually, Hachikuji herself doesn't really feature in this first episode of the arc at all - instead, merely her backpack become a prominent part of the episode after Hachikuji apparently left it behind after visiting Araragi at his home. As Araragi tries to find the rightful owner of said iconic backpack, he comes across Yotsugi Ononoki, who is thankfully wandering around without her sister and has also vowed never to deliver a posed look. Ononoki seems to be rater interested in Mayoi overall - how she came to be a ghost, why she might have forgotten her backpack, and perhaps most importantly why she's still a ghost despite Araragi having resolved her problems back in the first season.
All of this questioning has also left Koyomi pondering about Hachikuji's past and current feelings, so much so that he seems to have completely forgotten the small problem of some summer homework that needs doing, but which he no longer has time to complete. Luckily for him, Shinobu is on-hand to suggest a solution to the problem - a spot of time travel back to the previous day so he can get it done. This pocket-sized vampire is certainly able to live up to her word and send them both back in time without doing much difficulty, but returning may be another matter entirely, and it seems as if the duo's destination has been overshot by a rather considerable amount...
By this franchise's standards this was a pretty quiet episode of Monogatari Second Season - it had a few nicely delivered moments, and it was really enjoyable watching the developing relationship between Araragi and Shinobu (which seems to flow better than it has previously), but Ononoki's appearance was perhaps a little protracted and Ougi's introduction a little confusing. Still, the episode leaves us with a nice little cliff-hanger to what looks set to be Hachikuji's origin story, which certainly seems ripe with potential that the show can hopefully deliver on.