Re: Approved: Citi Hilton HHonors Visa Signature Card
The $6k only limits the amount you can carry as revolving debt on that no pre-set spending limit card. Depending on how that issuer sees you in their internal records, you can far exceed that $6k limit, but you must pay off anything in excess of that $6k limit by the due date, in addtion to any minimum you'd be expected to pay on the $6k limit.
(I think I got that right, but it's open to clarification from others here, of course!)
Read the card agreement that they send to you for more accurate info on how this works.