。
She came in second in the race.
Literal
She [topic-は] race [in-で] 2nd-place [result-に] became.
The counter 着 ranks finishing positions in races — 一着, 二着, 三着 are first, second, third place. It comes from 到着 ('arrival') and applies primarily to horse races (where it's the standard way to describe finishing order) and by extension to footraces and other competitions. The で here marks the 'arena' or scope of the event — the race is where this finishing happened — and the になる construction is Japanese's standard way of saying 'ended up as' or 'became.' Half-width '2着' would be more typical in writing today, but the full-width ２ in the original text is the older typographic convention still common in Japanese print.