Hang by a thread means to be in a very uncertain or dangerous state. The correct answer is this meaning because the expression is used figuratively, not only by its literal words.

Examples:

• The peace agreement was hanging by a thread.
• In an HSC essay, Hang by a thread can express this meaning: to be in a very uncertain or dangerous state.
• When this expression appears in a passage, connect Hang by a thread with the idea of to be in a very uncertain or dangerous state.