。
She hates speaking in public.
Literal
She [topic-は] in-public [at-で] speaking [nominalizer-こと] [subject-が] disliked.
The na-adjective 嫌い takes its object with が rather than を — 話すことが嫌いだ, not *話すことを嫌いだ. This が-marking pattern applies to a family of evaluation predicates: 好き, 嫌い, 上手, 下手, 怖い, 欲しい, and others. What English treats as the direct object ('I hate speaking') is grammatically the subject of the Japanese adjectival predicate.