Option 1 -> "Carelessly" means without attention or care, which contradicts the idea of understanding every detail.
Option 2 -> "Lazily" implies lack of effort or energy, inconsistent with ensuring comprehension of all details.
Option 3 -> "Attentively" means with careful attention and focus, which aligns perfectly with understanding every detail.
Option 4 -> "Abruptly" means suddenly or sharply, which doesn't logically describe the manner of listening.
Hence, Option 3: attentively -> The context clearly indicates the students were focused and careful, as evidenced by "ensuring that they understood every detail." Attentively is the only adverb that describes listening with concentrated attention and care -> correct