。
She walked away without even saying goodbye.
Literal
[topic-は] greeting [even-も] without-doing departed.
挨拶 covers both 'hello' and 'goodbye' in Japanese — it's the catch-all for any social greeting, including the ritual exchanges that bookend an encounter. せずに is the negative ず-form of する with the connecting に, meaning 'without doing.' The particle も here is the negation-emphasizer 'even' — 挨拶もせずに literally says 'without even doing a greeting,' a stronger condemnation than just '挨拶しないで.' 立ち去る is a compound verb, literally 'stand-and-leave,' that conveys leaving in a deliberate, physical way (often with a touch of indignation). The whole sentence paints a picture of conspicuous rudeness in a culture where greetings are considered essential.