Single pilot reported an NMAC event during landing practice on the right downwind pattern for runway 26. The opposite direction aircraft mistakenly entered the left downwind for runway 8 which resulted in the traffic passing within 200 feet.

Narrative

I had been practicing pattern work and touch and go's at my home airport (ZZZ). Another aircraft was in the pattern and was also practicing touch and go's. Our aircraft were communicating our positions in the pattern. A third aircraft called on frequency and reported his position and was going to enter the traffic pattern. The traffic pattern was RIGHT traffic for runway XX. However; the aircraft (CESSNA 182) that announced joining the pattern was confused and entered the traffic pattern for the opposite runway although announcing he was entering a RIGHT DOWNWIND for Runway XX he was actually entering a LEFT DOWNWIND for runway XY. My passenger; spotted the approaching aircraft at our 12 O'clock position on our DOWNWIND leg. The wrong direction aircraft passed our aircraft about 200 feet to our right side; same altitude; going the opposite direction. I contacted the aircraft and informed him he was downwind for the opposite runway and that he just past me going the opposite direction very close. He responded he was going to make a RIGHT 180 and then we would both be 'on the same page'. I landed my aircraft safely. I believe the wrong way pilot was unfamiliar with the landing airport and was confused with the airport traffic area.