You can set the article as "Registered", which will then require the user to login to your site. Then, in your category view, I believe you want to enable a setting like "Show unauthorized links". That will show the intro text of the article in the blog view, but when clicking into it, the user will be brought to the Joomla Login page. From there, they can either login with their Facebook credentials or their Joomla credentials (if they have them).
Unfortunately, you can't use the Like button to 'gate' content. That's a violation of Facebook's terms of service.
That's the only recommendations I'd have. There is no way with JFBConnect to 'hide' content optionally. We use Joomla underneath, and their access permissions. So, either something is hidden to guests or it's visible. There's not a way to tell K2 not to show it to guests and then, later on, allow the same guest to see it. That would have to a change in K2 itself.
Hope that explains,
Alex
Connect with Facebook or Like to view article k2
