Step 1: Define the word "Demure".
"Demure" is an adjective used to describe someone (usually a woman) who is reserved, modest, and shy. It often implies a certain quiet and polite behavior.
Step 2: Evaluate the options.
Withdrawn: Not wanting to communicate with other people. While related, it can imply sadness or anti-social behaviour, which "demure" does not.
Shy: Nervous or timid in the company of other people. This is a core component of being demure.
Brazen: Bold and without shame. This is an antonym.
Brash: Self-assertive in a rude, noisy, or overbearing way. This is also an antonym.
Step 3: Choose the closest synonym.
"Shy" is the closest and most fitting synonym for "demure" among the choices.