Final answer:
The literary device exemplified by the phrase 'Before the indifferent beak could let her drop' is personification.
Step-by-step explanation:
The phrase 'Before the indifferent beak could let her drop' exemplifies the literary device of personification. Personification is a figure of speech where human qualities are given to animals, objects, or ideas. In this phrase, the beak is being credited with the human trait of indifference, which means it's being treated as if it has human feelings or reactions, even though it cannot truly be indifferent as it is not human. This is quite distinct from a simile that would use 'like' or 'as' to make a comparison (e.g. 'like an indifferent person' would be a simile), or a metaphor which would make a direct comparison without using 'like' or 'as' (e.g. 'the beak is the face of indifference'). Synesthesia involves the crossing of sensory boundaries (like hearing colors), and it is not applicable in this context.