。
She really hates carrots.
Literal
She [topic-は] carrots [subject-が] greatly-disliked is.
大嫌い ('really hate, can't stand') is the intensified form of 嫌い ('disliked'), the negative counterpart of 大好き. Like its positive twin, 大嫌い is a na-adjective taking が for the disliked object. Note the orthographic shift between this sentence and the previous form: にんじん in hiragana (more conversational, food-context) vs ニンジン in katakana here. Both are valid for the same word; the katakana form is more common in scientific or culinary writing, while hiragana is everyday. Carrots show up almost universally on Japanese children's lists of disliked vegetables — 子供の嫌いな野菜 surveys consistently rank them near the top.