。
She walked out without even saying goodbye.
Literal
She [topic-は] goodbye [also-も] not-saying went-out.
The grammar piece here is ~ずに or its bare form ~ず — the classical/literary negative te-form, meaning 'without doing X.' Here 言わず ('not saying') chains directly into 出ていった ('went out'). The も marks 'even' — not even saying goodbye. 出ていく is a compound verb (出る 'exit' + いく 'go') stressing the going-away direction. Saying farewell carries social weight in Japan: leaving without a clear さよなら, またね, or 失礼します signals real annoyance, hurt, or emotional withdrawal — it's not a neutral exit. The bareness of the sentence captures the chill of the moment.