。
She managed to open the box.
Literal
She [topic-は] that box [object-を] open [nominalizer-こと] [subject-が] could-do.
~ことができる is the formal, written-register way to express ability — 'can do X' built up from こと nominalization plus できる ('be possible'). For everyday speech, the potential form (開けられる) is shorter and more natural; ~ことができる is preferred in writing, in polite contexts, or where the verb's potential form would be ambiguous. Past tense できた here suggests the success of an attempt, especially with a verb like 開ける ('open') that can imply effort against resistance.