give one's right arm 不是简单地认为是给出右胳膊，因为右手对于大多数人都至关重要，给出了右胳膊，即给出了所有，所以这个短语多引申为“付出极大的代价”。

【例句】
To gain such achievements, he gave his right arm.
为了取得这样的成就，他付出了极大的代价。

I'd give my right arm to have that bike again. I never should have sold it. Without it, I can't go anywhere conveniently.
我愿意付出极大的代价拥有那辆自行车。我不该卖掉它。没有它，我哪儿也不方便去。