from the pic - https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2F…
1 end goes into the tap outlet - I have
1 end goes into hose gun - does Not fit - when I try put it will not go in - need specials adapter - from bunnings- the hose gun does fit into an old conventional such as - https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2F…
Pretty sure this will do the job for you…
https://www.bunnings.com.au/aqua-system-hose-fit-brass-set-4…
Some additional examples of what can be purchased:
https://netagarden.com.au/products/category/brass-hose-fitti…
The hose looks like (probably)standard tap threaded fitting. You just need the adaptor to go to a quick fitting. They are available in Bunnings for a couple of dollars. Some guns have an adaptor screwed into them.
OP, take your weird hose to Bunnings, look in the hose fitting sections, and see what fitting fit it.
I just worked it out , after a friend showed me one already connected , No need for any adapters - these metal fitting for the Nozzle - need to be pushed down & then inserted . Problem solved !!
If you have a regular hose like this, you can cut off one end (or remove that screw attachment) and it'll fit into these attachments. You unscrew the bottom of the attachment, shove the bare end of the hose and screw the bottom part back in. That bottom part, when screwed in, will grip the hose. Like this > https://www.youtube.com/watch?v=HR8OkhLhtYo
I'm not sure if it'll work on that strange-looking hose you've got in the first picture though.