。
She really hates green peppers.
Literal
She [topic-は] green-peppers [subject-が] greatly-hate is.
ピーマン looks like an English loanword but actually comes from French 'piment' (originally meaning chili pepper, though Japanese narrowed it to bell peppers specifically). The word arrived during Japan's late-19th-century opening to European agriculture and stuck. ピーマン is a children's stereotypical disliked food in Japan — the slight bitterness of the green ones makes them famous as a vegetable that kids leave on their plate, alongside にんじん (carrots) and しいたけ (shiitake mushrooms). 大嫌い ('really hate') uses the prefix 大 ('big') to intensify 嫌い ('dislike'); 嫌い is grammatically a na-adjective and takes が to mark its target — one of the patterns where Japanese diverges from English's 'hate (object).'