The question tests knowledge of correct prepositional usage with the adjective 'keen'. Keen means having or showing eagerness or enthusiasm. In English, certain adjectives combine with specific prepositions to form idiomatic phrases.
The correct preposition to use with 'keen' when expressing interest or enthusiasm for an activity is 'on'. Therefore, 'She is keen on learning new languages' correctly conveys her strong interest. This is a standard idiomatic expression.
The other options are incorrect: 'Keen in' is not a recognized idiom for expressing interest in an activity. 'Keen at' is sometimes used to describe skill (e.g., 'keen at sports'), but not general enthusiasm for learning. 'Keen for' typically means eager for something to happen (e.g., 'keen for a holiday'), which doesn't fit the context of being interested in an ongoing activity.