Carbon Dating, carbon dating is a from of dating in which you take the Fossil or bones of a animals and date it based on it's carbon decay.
This passage suggests that Inglis, despite her goals for change, is afraid, and realizes the challenge of her situation.
She wants to not only change Apartheid, but change the heart and perspective of the guard at her sister's jail, though she knows fully-well that this is going to be a difficult task. She also fears what will happen if she is unable to soften him.
This answer would be pre-writing
