。
She cheered for her favorite horse.
Literal
She [topic-は] her own favorite horse [object-を] cheered-for.
ひいき ('favoritism, patronage') prenominally modifies a noun to mark it as one's favorite — typically applied to performers, sports teams, restaurants, and animals at the racetrack. 応援する ('to cheer for, support, root for') is the standard verb for active support of a competitor or cause. The pairing places the scene squarely at the racetrack — a small, vivid theater of stake and spectacle.