。
She cherishes that flower.
Literal
She [topic-は] that flower [object-を] very treasured-doing.
大事にする ('to treasure, take good care of, value') applies to objects, people, relationships, time — anything you don't want to neglect. The verb makes a natural pair with 大切にする, near-synonyms with subtle shading: 大切 leans more emotional ('precious to me'), 大事 leans more practical ('handle carefully'). The ~ている here marks ongoing state — 'is in the state of treasuring it'. とても ('very, deeply') intensifies the regard; without it, 大事にしている reads as plain 'is taking care of'.