。
She glanced casually at the book.
Literal
She [topic-は] that book [to-に] casually eyes [object-を] sent.
目をやる ('send one's eyes' to something) is the standard idiom for casting a glance — a quick, deliberate look in a direction. 何気なく ('casually, offhandedly, without any particular thought') is the adverbial form of 何気ない, capturing an unstudied, in-passing quality. The combination paints a moment of incidental notice — not a stare or close inspection, just the eyes flicking that way. The same やる appears in other directional set phrases: 心を遣る ('extend a thought'), 思いをやる ('cast one's mind').