She could answer any question she was asked.

Literal

She [topic-は] asked things [contrast-は] any thing [even-でも] answer could.

聞かれたことはどんなことでも — 'whatever things she was asked' uses the relative clause 聞かれた modifying こと, with どんなことでも ('any kind of thing at all') reinforcing the universality. ことができた is the formal potential.