The scoring system used in a game of rugby league awards points based on specific actions: a try scores 4 points, a conversion kick adds 2 points, a penalty kick is worth 2 points, and a drop goal earns 1 point. A try is scored when a player grounds the ball over the opposing team's goal line. Successful conversions follow tries, allowing teams to increase their score. This scoring structure emphasizes strategic play, making the game dynamic and engaging for both players and fans alike.