The phrase "show someone the door" means to ask someone to leave or to dismiss someone from a situation or a place. There are several synonyms that can be used to convey the same meaning, depending on the context and the level of formality desired. Some synonymous phrases include "kick someone out," "escort someone out," "ask someone to leave," "give someone the boot," "send someone packing," and "show someone the exit." These phrases can be used in various settings, such as a workplace, a social event, or a public space, to indicate that someone is unwanted or has overstayed their welcome.