They now have their own ____ website.
it's a compound adj...so the the right answer should be a full-fledged website
* the use of a (-) is necessary*
it modifies the noun "website" so that's adjective. fully fledged and fully-fledged are not right answers. let's choose among full fledged and full-fledged. It's a compound noun so (-) has to be used.