μετακομίζω ==> first thing that comes to mind is 'move to another house', but could also be used for 'move to another country'. μετακινώ ==> I move sth from one place to another e.g. Μετακινώ το γραφείο μου στο σαλόνι (I moved my desk to the living room) κουνάω ==> to cause sth to move, or to move e.g. Κουνάω τα χέρια μου (I move/swing my hands) κινάω ==> to set sth in motion e.g. Οι μύες κινούν τα μέλη του σώματος (The muscles set the parts of the body in motion) (there are also loads of phrases with 'κινώ' but they're too many to write here :D) "κουνάω τα παπούτσια" ==>no I wouldn't say this one. It sounds as if you move them to and fro or sth, so it doesn't really make sense. But if you say 'μετακινώ τα παπούτσια' it would mean I take the shoes and put them somewhere else. So this is what you want!