。
She didn't know either his address or his phone number.
Literal
She [topic-は] his [genitive-の] address [also-も] phone-number [also-も] didn't-know.
The ~も~も pattern with a negative predicate gives the 'neither...nor' reading: 'neither his address nor his phone number.' Without も (with を) it would just be 'didn't know his address and phone number' — flatter. The doubled も emphasizes that both are missing. 知る ('know') in its negative past 知らなかった simply states the past lack of knowledge.