By any stretch of the imagination means by any possible interpretation or effort of thinking. The correct answer is this meaning because the expression is used figuratively, not only by its literal words.

Examples:

• It is not a complete solution by any stretch of the imagination.
• In an HSC essay, By any stretch of the imagination can express this meaning: by any possible interpretation or effort of thinking.
• When this expression appears in a passage, connect By any stretch of the imagination with the idea of by any possible interpretation or effort of thinking.