It's a dual Hyperglide/Uniglide hub, manufactured around 1989.
If it's a Dura-Ace, then it was 8 speed and you can use a 9s cassette. If not DA, then IIRC all the lower group dual hubs were 7s, (before they went exclusively to HG), so you're stuck with either 7s, or using 8 cogs of a 9s cassette, but with a 9s shifter. At ~ 3cm, it looks like you have a 7s freehub body.
Now, since it's not DA, you can swap out the freehub body pretty easily. It'll probably run you about $30 if you do it yourself.
Freewheels do not go on freehubs.

Oh, and The Cars have a new album out.