Jamieson, Fausset and Brown on 1 Corinthians 16:9

9. door--(2Co 2:12). An opening for the extension of the Gospel. Wise men are on the watch for, and avail themselves of, opportunities. So "door of hope," Ho 2:15. "Door of faith," Ac 14:27. "An open door," Re 3:8. "A door of utterance," Col 4:3. "Great," that is, extensive. "Effectual," that is, requiring great labors [Estius]; or opportune for effecting great results [Beza].

many adversaries--who would block up the way and prevent us from entering the open door. Not here false teachers, but open adversaries: both Jews and heathen. After Paul, by his now long-continued labors at Ephesus, had produced effects which threatened the interests of those whose gains were derived from idolatry, "many adversaries" arose (Ac 19:9-23). Where great good is, there evil is sure to start up as its antagonist.