Final answer:
The correct punctuated sentence is 'I appreciate your talking to the client while I was out of the office.'
Step-by-step explanation:
The correctly punctuated sentence is:
I appreciate your talking to the client while I was out of the office.
This sentence is correct because it uses the possessive form of 'your' to indicate that the talking was done by the person being addressed. The possessive form 'yours' should not be used in this context.
Learn more about Correct punctuation in a sentence