Do NOT(!) under ANY circumstances, fit a star-fangled nut inside a carbon steerer tube. If you do, it’ll likely break off when you’re at high speed and kill you, planet Earth will implode and all human life will be gone.
Seriously though – you should NEVER install an SFN in a carbon steerer – it’s dangerous.
The expansion fitting you pictured sits inside the steerer tube and if you look closely you’ll see there is a 6mm hex/allen fitting inside, and further inside that is (usually) a threaded section for a 5mm allen screw – although yours looks like it has an external threaded section which the top cap screws onto.
Fit the expander bung into the steerer tube at the appropriate height (after you have measured and trimmed the steerer to length), tighten the 6mm allen to secure it in place. This needs to be snug/tight, but not forced too tight.
The top cap is then fitted, the screw going into the expansion bung.
It’s very easy once you have done it once but really this is not something to mess with so if you’re not sure it’d be best to take it to your LBS and pay them £10 to do it.