I'm not sure you have the capability to accomplish it regardless how much and how good of instructions you receive. Have you tried using the room while door is open? Have you tried leaving door open when room isn't in use then closing when in use? Privacy is usually only required for a few minutes and that isn't long enough for temperature to change dramatically. If climate is extremly cold in Winter you might consider a small ,portable ,electric space heater. Maybe someone can explain well enough and you can do it,meanwhile here's an option to think about that imo an inexperienced person has better odds of pulling off. It's called "jumper vent or jumper duct". If walls are drywall, buy 2 small vent covers then cut a hole in wall near ceiling in room that is presently airconditioned and a secound hole near floor in powder room ( BOTH HOLES IN SAME STUD CAVITY). Reach in to caulk as much joint as possible between stud and drywall. Mount a small fan inside either hole that can be reversed at will by removing cover. Supply fan with extension cord taped to baseboard. In Winter position fan to move air from air conditioned room and exhaust to powder room, in Summer vs vs. There's usually enough gap at bottom of door to allow air return but if not cut an inch off door.

Klem's idea about a jumper duct is an easy DIY fix for the issue. It's also referred to as a deKiefer bypass or transfer duct.

https://buildingscience.com/documents/information-sheets/information-sheet-transfer-grilles-and-ducts

If using such a transfer duct, one could add a thermostatically controlled blower fan such as below to keep air circulating through the powder room:

https://www.amazon.com/gp/product/B0792QR5YT/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

The vent blower normally works like this; in the summer, when it senses cold air in the duct, the fan comes on to boost cool air into the room. In the winter, when it senses warm air in the duct, it turns on to boost the warm air into the room. The summer and winter settings are switched appropriately in the spring and fall for the oncoming season. In Klem's application, the summer setting would be used in the winter; when the fan sensed coolness, it would boost warm house air into the room. Likewise, one would use the winter setting in the summer; when the fan senses warmth it would boost the cooler house air into the room. The fans are quiet as well as they are not on/off controlled, when a setpoint is reached the fans start slowly and increase in speed as the delta from the setpoint increases.

I used the vent fan in another way. I reversed the location of the thermistor temp sensor (from the duct to the room side) and physically reversed the fans to blow into the duct (all easy to do). I placed the unit in an exhaust duct in my TV electronics closet, set it on the winter mode, and it exhausts the warm air from the electronics when the closet warms up (pulling cooler room air in from under the door).

Tiny powder rooms really don't need and rarely have supply ducts. I have one in a 20 year old build and it doesn't have one. Keep the room open when not in use, 5 or 10 minutes of use is unlikely to require further heat or cooling for comfort.

If you want conditioned air when in use, turn on the exhaust fan.

Get a 12" to 4-6" "Y" adapter. Then get a short length of flexduct to insulate the take off.

Congrats on the new powder room addition! It sounds like a neat little space you're working with. Now, onto the HVAC setup – to split off from the existing 12"" flexduct, you'll want to use a Y-shaped junction or a reducer to transition to a smaller diameter flexpipe. Measure carefully to ensure a snug fit and maintain airflow efficiency.If you're not too confident in tackling this yourself, consider consulting with an HVAC professional. They can provide expert advice and ensure the job is done correctly. If you're looking for reputable HVAC leads in Las Vegas, you might find some helpful resources through this link. Best of luck with your project, Olga! ( https://pro.aroundwire.com/hvac-leads-las-vegas )