An idiom is a phrase or an expression that has a meaning different from the literal meaning.
Option C: 'Face the music' is an idiomatic expression that means 'to be confronted with the unpleasant consequences of one's actions'.
It forms a complete and meaningful sentence here. Hence option C is correct.
Options A, B and D:
'Face with music', 'face at the music' and 'listen to the music' are not idiomatic expressions. They have a literal meaning, and do not form a complete meaningful sentence.
Hence options A, B and D are incorrect.