Final answer:
Katniss shows her archery skills to the Gamemakers by shooting an arrow at the apple in a roast pig's mouth, which captures their attention and earns her a high rating.
Step-by-step explanation:
In The Hunger Games by Suzanne Collins, during her private session with the Gamemakers, Katniss Everdeen showcases her impressive archery skills. Frustrated by the Gamemakers' lack of attention, she shoots an arrow at the apple in the mouth of a roast pig on their banquet table, which gains their full attention.
This act of defiance and her exceptional shooting ability drastically improve her rating from the Gamemakers, positioning her as a formidable competitor in the arena.