I purchased CS5 in April of this year... At purchase I was informed I could get a free upgrade to CS6 ... How do I upgrade?
That sounds like an online store. If so, have you tried logging on to your account, and checking 'My orders'? I am not sure how the free upgrade would work, and I have a feeling that trying to phone Adobe is going to be a long and frustrating experience.
There are quite a few Google hits HERE
North America
Europe, Middle East and Africa
Asia Pacific