I'm asked to do an adventure I've already done

@BillFlowerpot  The game is supposed to block sims from receiving quests they've already completed, but that doesn't always work correctly.  In this case, if your sim has in fact finished the last part of the quest and the game does recognize it, that could be the reason it can't complete again.  Regardless, there's nothing else to do here except cancel the quest and find another.

In the future, if an earlier step of a quest is stuck, you can use NRaas DebugEnabler to grant the next step and therefore force-complete the stuck one.  But I'd suggest just not accepting any quest that your sim has already completed unless it's one of those simple deliver-these-items options that are supposed to be repeatable.

Thank you Puzzlezaddict for your response.

Upon my return to China the I received a fanfare, and the quest was taken from my in-tray. I thought that it had worked after all, however, when I answered my phone, it was for the very same request. Would you please explain more how I can use Nrass DebugEnabler.

Yours BillFlowerpot

P.S. I have all tomb sigils for China along with all vases, however, I only have one of the drop stones 

@BillFlowerpot  To force-assign the next step of a quest (or any opportunity), click on the sim and select NRaas > DebugEnabler > Opportunities, then choose the next opportunity in the chain.  Sometimes it's not clear from the names which one you want to choose, so save before doing this and quit if you pick the wrong one, or just cancel that quest and try again.

Thank you for taking the time to respond to my post. I tried using NRaas > DebugEnabler > Cellphone Opportunities > Opportunities > etc., but without knowing what I was looking for, I found the lists daunting.  During game play it seemed to resolve itself, for a while. However, I was still getting quest requests for ones I had already done.  Some of which were not resolvable because I had already found the item required and bulldozing and replacing the tomb did not always work.  It became a problem when these were the only quests I was offered.   Somewhere, somehow the adventure data got corrupted.  I have since saved my Sim to the library and started a new game without 'World Adventures' in my current lineup.  In order to save hard drive space I have deleted all saves therefore there's no going back.

After saving my sim to the bin and starting a new game I tried again with the same sim, however, when I went on my first quest 'Tomb Of The Lost Army' (Within the walls of the forbidden city), I found the tomb already open. Furthermore, the artifact I was looking for was not in any of the treasure chests.   I went to the dragon's cave and the hidden door was also open. I therefore am of the opinion that the sim had become corrupt.

@BillFlowerpot  That's possible, and unfortunate.  But in general, it's possible to reset tombs and play through them again even within the same save, so tombs in a different save should be unaffected.