。
She just knew it intuitively.
Literal
She [topic-は] sixth-sense [by-で] that [subject-が] understood.
第六感 ('the sixth sense') is the standard Japanese term for intuition or a hunch — a borrowed concept that's settled into everyday vocabulary. で here is the instrumental/means use ('by means of, with'). 分かる ('understand, become clear') takes its 'thing understood' with が — that surprises learners used to using を for the object of 'understand.' This is the same が-marked-object pattern seen with 好き, 嫌い, 怖い, 上手, etc.