The antonyms for the word "puzzling over" could be considered as understanding, comprehending, or grasping. These terms suggest a sense of clarity and comprehension, where one has no difficulty with a particular subject or problem. Instead of pondering or struggling, one can quickly assimilate what is being presented or understood. Other antonyms might include accepting or believing, suggesting a more passive, confirmatory stance towards a fact or concept. Ultimately, the antonyms of "puzzling over" represent the opposite of uncertainty and confusion, instead highlighting clarity and ease of understanding.