If you are sympathetic to someone who is in a bad situation, you are kind to them and show that you understand their feelings.
She was very sympathetic to the problems of adult students.
她对成年学生的问题表示同情。
If you are sympathetic to a proposal or action, you approve of it and are willing to support it.
Many of these early visitors were sympathetic to the Chinese socialist experiment.
有很多早期的访问者都赞同中国的社会主义实验。