She was able to distract herself from various anxieties.

Literal

She [topic-は] various anxieties [from-から] attention [object-を] divert was-able.

気を紛らわせる (きをまぎらわせる) is a set expression using the causative of 紛れる ('to become diverted'). 様々の (さまざまの, 'various') is a na-adjective.