。
She's extremely interested in music.
Literal
She [topic-は] music [in-に] very interest [object-を] is-holding.
~に興味を持つ ('to take an interest in / to have interest in') is the active framing of interest — to actively hold the interest, as opposed to passively having it. Pair this with ~に興味がある ('to have interest in,' a more static state-of-affairs framing) and you have a productive pair. 非常に ('very, extremely') belongs to a slightly elevated register; in casual speech とても is more typical.