Does the brass fitting on the can adapter screw into the adapter, or push in? Basically you need to adapt the air brush hose to your compressor on the low pressure side of that pressure regulator. If the fitting on the end of the air brush hose is threaded where it goes into the can adapter, you can either use bushings to reduce the size of the fitting in your pressure regulator to the size you need for the air brush hose, or you can get a brass plug to fit into the air fitting for your pressure regulator and drill and tap it to fit your air brush. It looks like the plastic hose for the air brush is a push on fit over the fitting. If the fitting is a knurled push in on the plastic adapter for the pressure can, remove it from the can adapter, and remove the plastic hose from the brass adapter. Then get a brass plug to fit the air hose quick connect that would plug into your pressure regulator's female quick connect fitting. Drill the plug for a slip fit of the air brush hose fitting, and solder it into the brass plug. When you screw the modified brass plug into the fitting, and plug it into the pressure regulator, all you need to do is push the air brush hose back over the top of the fititing.
Before you do a bunch of modifications though, did your air brush come with any paperwork? My badger air brush that I bought from a Snap On dealer 20 years ago came with an adapter to plug into a pressure regulator/moisture trap on my compressor. If yours didn't, badger probably offers the parts you need.