、。
She wanted to peek, but she just couldn't.
Literal
She [topic-は] peeked want [but-が], such thing [contrast-は] could-not-do.
覗き見する combines 覗く ('peek') with 見る ('see, look') as a fused noun-verb — 'sneak a look.' ~たかった is the past tense of the desiderative ~たい ('want to'). そんなことはできなかった emphasizes the inability — そんなこと ('that kind of thing') is the topic, with は marking it contrastively.