According to the picture of that hose, the description is wrong. The description says the hose has a 3/8 male flare connection, but the picture shows it as female.
And then your description says you are looking for a female adapter, but your picture seems to show that what you really need is a male adapter to go into that tee.
It looks like that the flare end of that hose should screw into the fitting on your firepit.
Also, coming out of your house you should really have a shutoff valve. It looks tight, but hopefully if you removed the pipe strap you can pull the pipe out enough to spin on a ball valve and the fittings that you need to get to that hose. Maybe you could go with a 3/8" shutoff valve to save some room.
So, here's what I would suggest (listed in order with coming out of your house)....
3/4" x 3/8" black malleable bushing
3/8" black iron close nipple
3/8" threaded ball valve
another 3/8" black iron close nipple
then your hose going to your fire pit.
Hope this helps. Keep in mind that you will need a conversion kit to run that fire pit on natural gas. You can't just replace propane with natural gas and hope it will work.
