From prō- + mittō (“to send”). Compare typologically Ancient Greek ἐπαγγέλλω (epangéllō) (< ἀγγέλλω (angéllō, “to carry, deliver”)); сули́ть (sulítʹ) (perhaps akin to слать (slatʹ, “to send, dispatch”)).
Practice speaking and memorizing "promitto" and many other words and sentences in Latin.