Opposite words for unintelligibly:
understandably, clearly, intelligibly.
Usage samples:
  1. We must reduce our volume to the simple evangelists, select, even from them, the very words only of Jesus, paring off the amphiboligisms into which they have been led, by forgetting often, or not understanding, what had fallen from him, by giving their own misconceptions as his dicta, and expressing unintelligibly for others what they had not understood themselves.
    "Memoir, Correspondence, And Miscellanies, From The Papers Of Thomas Jefferson", Thomas Jefferson.
  2. " From Africa- from a blind woman," answered Geronimo, almost unintelligibly.
    "The Amulet", Hendrik Conscience.
  3. Rosa- He began to mutter unintelligibly, his vitality flared up, and it was with difficulty that Norine could hold him down.
    "Rainbow's End", Rex Beach.
  4. Bob merely grunted unintelligibly, and Della retired in a high state of indignation, resolved to give the boys a " piece of her mind" when finally they should arise.
    "The Radio Boys with the Revenue Guards", Gerald Breckenridge.