Option 1: admiringly -> suggests respect but doesn't capture the eager intensity of "hanging on every word."
Option 2: avidly -> means eagerly and enthusiastically, perfectly matching the intense interest shown by hanging on every word.
Option 3: thoughtfully -> implies contemplation but lacks the eager, absorbed quality described in the sentence.
Option 4: anxiously -> suggests worry or nervousness, which contradicts the positive engagement with the speaker's words.
Hence, Option 2: avidly -> "Avidly" means with great enthusiasm and keen interest, which precisely describes someone who hangs on every word as if receiving life-changing information. The adverb captures both the intensity and the eager absorption that characterizes this type of listening -> correct