方違え is read as かたたがえ (katatagae) and means setting off the night before one normally would have departed, travelling in a different direction, spending the night there, and leaving for one's destination in the morning (done to avoid travelling in an unlucky direction; a common practice during the Heian period).
かたたがえ
katatagae
かたたがい
setting off the night before one normally would have departed, travelling in a different direction, spending the night there, and leaving for one's destination in the morning (done to avoid travelling in an unlucky direction; a common practice during the Heian period)