。
She wrote the date in numerals.
Literal
She [topic-は] date [object-を] numbers [with-で] wrote.
数字で uses で in its instrumental sense — 'with numerals, in the form of digits' (as opposed to spelling out in kanji or words). Japanese makes a frequent practical distinction between 数字 (Arabic numerals: 1, 2, 3) and 漢数字 (kanji numerals: 一, 二, 三).