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She probably won't be able to forget hearing that sad song.
Literal
She [topic-は] that sad song [object-を] heard [nominalizer-こと] [object-を] won't-be-able-to-forget [probably-だろう].
The whole act 'hearing that sad song' is nominalized with こと and made the object of 忘れる: she won't be able to forget the experience of hearing it. 忘れられない is the negative potential of 忘れる ('forget'), itself the kind of verb whose potential form is more common than its bare form when discussing emotional memory. ~だろう ('probably, I'd say') hedges the prediction — the speaker is offering a confident guess, not stating a fact. 曲 here means a piece of music or song; without lyrics specifically, it could be instrumental. Music that affects you that deeply tends to lodge there.