Fathom out means to understand something after thought or investigation. The correct answer is this meaning because the expression is used figuratively, not only by its literal words.

Examples:

• The detective tried to fathom out the mystery.
• In an HSC essay, Fathom out can express this meaning: to understand something after thought or investigation.
• When this expression appears in a passage, connect Fathom out with the idea of to understand something after thought or investigation.