However, you could imagine Katniss liking music based on her personality and the world she lives in.
* Considering her personality: She's resourceful, independent, and resilient. She might appreciate music that reflects those traits: powerful ballads, folk music, or songs with a strong rhythm.
* Considering her world: In Panem, music is probably used for propaganda and entertainment, but it's possible she might enjoy the folk songs of District 12.
Ultimately, what Katniss enjoys listening to is left up to your imagination. If you want to write a fan fiction or create your own headcanon, feel free to explore different musical possibilities!