。
She would rather listen to others than talk herself.
Literal
She [topic-は] [by-oneself-自分で] talk [more than-よりも] other people's talk [object-を] listen [want to-たい] [quotative-と] is-thinking.
~よりも~たい ('want to do Y rather than X') uses the comparison particle よりも (より + emphatic も) to set up a preference. The whole inner clause is wrapped in と思っている ('is thinking that') — a soft, characterizing way to attribute a preference. 自分で ('by oneself') here adverbially marks self-action — 'rather than (be the one to) talk herself.' A personality sketch: more listener than speaker.