Which Banner mod is this?
 

That will put a banner where indicated in the pic. For 3.8.7. Thanks.

I don't see a banner? O.o

In case you're serious, the banner would be where the red circle is.

Your topic title, and your picture imply its going to be shown. You can just use html in the description, no need for a mod.

Thanks.

If I need it to rotate and measure clicks, is there a specific mod for this location? or a one that will do various locations including the one I need?

You're still lloking at html, but you should look into a proper ad management solution. Nothing in vBulletin is going to be able to do that well.

Please recommend an ad management solution for 3.8.7.

You're not looking for an ad manager for vBulletin, you're looking for an ad manager, like openx