請問being用法

appreciate (解:感謝, 感激) 是及物動詞(transitive) 必須後接受詞(object) ，可加 動名詞(gerund)。

Your sentence has an error though. It should be rewritten as:
I appreciate your being protective of Katie.

("your being protective of Katie" is a noun phrase and the object of "appreciate") 感謝什麼? 感謝 "你對凱蒂的保護"

Reference: (Cambridge Dictionary)
- used when you are thanking someone or showing that you are gratefule.g. We really appreciate all the help you gave us last weekend.[+ -ing verb] I appreciate your making the effort to come.

2011-10-23 11:40:25 補充：
You are protective of Katie.
I appreciate it. (it = your being protective of Katie)

The use of being,to Anonymous is:-
We understand from the sentence "I appreciate you being protective of Katie" that it should be re-written that need to become the sentence as:-I appreciate your Katie being protected. and clearly it is word-order. And the agency if Indirect and Direct speech which should be Indirect before Direct="your" before" Katie" who would considered to be the receiver.Then the sentence would have been self -explainatory already.

being--->Gerund+passive voice
appreciate--->verb
so,cannot have a more verb
being protective --->I am protect by Katie,not I protect Katie!