She left home three days later.

Literal

She [topic-は] three-days later [time-に] home [object-を] left.

[Time period]+後 ('after, later') is the standard frame for offset times: 三日後 ('three days later'), 一年後 ('a year later'), 数時間後 ('a few hours later'). The に here marks the time-point of the action. Note 三日 reads as みっか, the irregular Japanese-origin reading for 'three days' — Japanese counts of days run on native readings up to ten (一日 ついたち, 二日 ふつか, ... 十日 とおか) and shift to Sino-Japanese readings beyond. The を on 家 marks the place left, with 離れる as the verb of departure.