How does her early encounter with peeta affect their relationship after they are chosen as tributes
In Suzanne Collins's The Hunger Games, Katniss and Peeta are both teens in District 12 when they become the district's tributes in the 74th annual Hunger Games, a competition in which children must fight to the death for the nation to watch. The ritual is meant to remind the districts of the government's power and to discourage rebellion.
Peeta's name is drawn, but Katniss volunteers in place of her sister Prim. Katniss is much stronger, mentally and physically, and is a skilled hunter; she believes young, delicate Prim would never survive and it is also her natural instinct to protect her little sister. Although both Katniss and Peeta are deathly afraid of participating in the Games, they enter the competition from different positions and perspectives since Katniss was a volunteer. She is sacrificing herself for her sister; Peeta is sacrificing himself for no particular person, so the sting of injustice hits him harder.
While Katniss and Peeta are a bit distant from each other at first, Katniss remembers Peeta's kindness to her in District 12 when they were younger. After Katniss's and Prim's father dies in a mine explosion, Katniss becomes the primary breadwinner for the family. Her mother is fragile, and Prim is just a small girl. On a particularly dire day, Katniss scouts town for scraps for the family to eat, and Peeta sees her, sitting in the rain with a look of desperation. Peeta throws some burnt bread to her, from the bakery his family owns and where he works. Katniss later figures out that Peeta saw her, and that he burnt the bread on purpose because he knew his parents would tell him to throw it out to the pigs. Katniss's discovery leads her to sympathize more fully with Peeta.
Over the course of the series, Katniss and Peeta are bonded by their shared experience in the Games and the rebellion, while Katniss grows further from Gale, who is certainly on board with the rebel cause but never had to fight for his life in the arena.