。
She began to find more pleasure in listening to music.
Literal
She [topic-は] music [object-を] listen-to [thing-こと] [from-から] more big pleasure [object-を] gain-began.
より大きな is the adverbial-comparative use of より meaning 'more, greater' — different from the standard より used in 'X より Y' comparisons. Here it has no explicit standard ('more than what?'), conveying a vaguer 'increasingly greater.' ~ことから marks the source of the pleasure: 'from the act of listening.' 得始めた combines 得る ('to gain, obtain') with the auxiliary 始める ('begin to'), producing 'began to gain.' The sentence reads as slightly literary, almost essay-like.