。
She left the room without saying a word.
Literal
She [topic-は] one-word [emph-も] not-saying [and-に] room [from-から] exited.
~ずに is the more literary/formal counterpart of ~ないで — same meaning, 'without doing X,' but feels tighter and more written. The two are interchangeable in many sentences but ~ずに has a slightly more elevated, often stoic tone. 部屋から出る uses から for the source/origin of motion (the room she leaves from); contrast 部屋を出る, where を marks a 'departure point' that one passes through.