what the very fuck

A variant of "What the actual fuck".

What the very fuck are 'ya doing?

what the possible fuck

You exclaim "What the possible fuck!" when you aren't completely sure that this potential fucked-up situation is actually happening or has happened or ever will happen. In other words, you don't want to completely commit yourself to whether this is an actual fucked-up situation or not because you don't have all the facts. And if you misjudge it or call it prematurely, you would look like a dick. So meticulous and cautious soul that you are "What the possible fuck!" is the perfect reaction.

While watching fake-news BSNBC, Pete phones his friend Joe.

Pete (breathlessly excited): "MadCow says that a swarm of little green moon-men have landed their spacecraft on Times Square and and are handing out little green lollypops while shouting 'Fear not! We've come in peace!'"

Joe (mildly dubious): "What the possible fuck!"