Are three airports or four required for private pilot cross country?
The regulation means you need to land at three separate airports.  This should include landing at your original departure airport at the end of the flight.

§61.109(a)(5)(ii)
One solo cross country flight of 150 nautical miles total distance, with full-stop landings at three points, and one segment of the flight consisting of a straight-line distance of more than 50 nautical miles between the takeoff and landing locations