Apalabrar, from palabra, word, is to agree on something by word of mouth. The Diccionario del español de México of El Colegio de México defines it as to commit to something or to contract it verbally. One of its examples: “Antes de firmar contrato se apalabraron sobre el precio del terreno” (Before signing a contract, they agreed by word on the price of the land).
De palabra, “by word,” the dictionary explains, means said but not set down in writing: prometer de palabra, to promise by word, resolver un asunto sólo de palabra, to settle a matter only by word. A person who is de palabra is “leal, honrado y cumplido” (loyal, honest and reliable).