2,i really appreciate your offering to help me, but i am sure that i will be able to manage it by myself.为什么用your用you不可以吗
what is the reason for your not coming on time
the reason for sth
your coming 你来
your not coming 你不来 都是事情的范畴
1)appreciate sb/one's doing sth 感激某人做某事
sb如果是代词,必须用宾格;one's指形容词性物主代词。
2)appreciate it that从句
i really appreciate you/your offering to help me都可以
传统语法用your加上动名词,在口语或非正式语体中,常用宾格代替所有格。