Hi L Doble,
I know what it means, but there is no direct translation that can go with it word for word because it loses all the connotations associated with it. I will tell you how to describe it though. First, literally, it means "he doesn't want to lose face". People from other countries will just understand this as "he doesn't want to feel embarrassed" or "he wants to take credit for all his actions".
As for the examples given, here are my descriptions:
1. Peter is too stubborn. He'll never admit he was wrong because he doesn't want to seem weak and discredited in front of other people.
2. Jenny has to much pride to be helped by other people. She wants everyone to know she can manage herself well and succeed in life.
3. He's too embarrassed to admit that his company isn't doing so well. He wants to be held in high regard.
Furthermore, as a bilingual speaker and teacher to Chinese students, I know that Chinese people like to "codify" and "generalize" actions into terms. This makes learning a language more complicated. In most cases, especially in English, you just have to describe in simple terms.
Hope this helps.