In the Tropics: the Moon, by Declination, can be either North or South of the Observer's Latitude; if it be North, East is on the Observer's Right; if it be South, East is one the Observer's Left.
Moving through North means it will move through the sky that is North of the Observer, whose back will be towards the near Pole, except in the Tropics,where both options are possible during any given month. of course, if one's Latitude is the same as the Moon's Declination,on that day, the Moon {or the Sun,for that matter} will seem to travel directly from east to West, with no shadows cast when overhead. The Eastern part will remain in the east until the Western part take over. see p 78 in the Book: the Moon is NE