This is the 5176th most frequent Korean word.
눈물로
"With tears" or "through tears."
Here, '눈물로' (with tears) indicates the cause or means (tears) through or by which something occurs (her face being wet).
그녀는 감동적인 이야기를 듣고 눈물로 얼굴을 적셨다.
She was moved by the touching story and her face was wet with tears.
In this sentence, '눈물로' (with tears) signifies the means or medium (tears) by which an action (expressing joy) is carried out.
그는 눈물로 기쁨을 표현했다.
He expressed his joy through tears.
The term '눈물로' (with tears) in this sentence expresses the instrumental role (tears) in achieving the result (softening the mother's heart).