。
She admitted to having heroin.
Literal
She [topic-は] heroin [object-を] is-holding [thing-こと] [object-を] admitted.
認める ('admit, recognize, acknowledge') takes the admitted content as a を-marked object. The content here is itself a clause — 'that she has heroin' — nominalized with こと. The chain ヘロインを持っていることを認めた reads literally 'admitted (the fact of) being in possession of heroin.' This use of こと is the formal, factual nominalizer (the alternative の would be more conversational and typically used for events-in-experience). 持つ in resultative ~ている marks the ongoing state of holding.