。
She wrapped both arms around his neck.
Literal
She [topic-は] his [genitive-の] neck [genitive-の] around [to-に] both-arms [object-を] wrapped-around.
巻き付ける is a 複合動詞 from 巻く ('wind, roll up') + 付ける ('attach') — 'wind around and stick.' Used for physical wrapping motions: arms around a neck, a scarf around a body, a snake around a branch. The に here marks where the wrapping lands (the destination). ~の回り ('around, the area surrounding') is a relational noun — 首の回り = 'the area around the neck.' 両腕 ('both arms') uses the prefix 両 ('both, two') common in body parts (両手, 両足, 両目).