Coincidentally I'm looking at that same bit of ducting.
I have my headlight switch out at the moment so I can see a bit more.
That "loose ducting" looks like this:-
View attachment 309969
The round end in the top left of the picture rests in a hole way up inside the dash just below the windscreen.
Looking up through the hole left by the headlight switch you can just about see where that round end goes. That light way up in the middle of the picture. Sorry. Not a very good picture.
View attachment 309973
Having that tube and the vent cover in my hand I can't see anything at all to reliably 'fix' things together.
I suspect the round end of the tube just rests on that round hole and the vent cover has (should have) some plastic tabs that clip it to the dash and that holds it all together.
My vent cover is loose - doesn't have any tabs/clips to hold it in place. When I reassemble I'll just put a strip of double sided tape along the edges.