The term 'box in a theatre' refers to a private seating area that is usually located at the side or rear of the auditorium. The crossword solution for this term is LOGE, which is a four-letter word. A LOGE is a type of box seating that is typically found in theatres and opera houses. It is usually located on the sides or rear of the auditorium and provides a more private and intimate setting for viewing performances.