The question popped into my head with this post where the woman in the pic has her hand one way and the rest of the folks had their hands the other way. Is there a rule for how it's done? I asked the same question there but no replies, so I was wondering if any history gurus can shed some light.
Yes, there is a rule for it (as with most things ceremonial Chinese).
In the Book of Rites, it clearly states that for males the left hand is to cover the right hand when greeting, while the opposite is done for females. This is because male (yang 阳) is linked to the left, while female (yin 阴) is linked to the right.
When doing a proper greeting, the arms are raised away from the body, with the covering hand's thumb hiding the other hand's thumb (ie. for males, the left hand's thumb would cover the right hand's thumb in addition to the left hand being placed over the right hand).
The only circumstance when the greeting is reversed is when it is done in mourning (at a wake, in times of disaster, etc). [from Rites of Zhou].