What does "fathom" imply?

The term "fathom" implies the ability to understand something deeply, often following considerable thought or analysis. In contexts where complex subjects or difficult problems are involved, to "fathom" means to achieve clarity and comprehension after engaging with the material. It suggests an active effort to explore and grasp the intricacies of a topic, leading to a deeper insight.

The other options do not align with the meaning of "fathom." For instance, remaining confused about a subject, avoiding deep thinking, or disregarding complexities all indicate a lack of understanding rather than the achievement of it. Thus, the choice indicating deep understanding after contemplation captures the essence of what it means to "fathom."