。
She started a conversation with the people in her neighborhood.
Literal
She [topic-は] neighborhood [genitive-の] people-(plural) [with-と] conversation [object-を] started.
会話 vs 話 vs 対話 — Japanese has several words for 'conversation' and the choice tells you the kind of exchange. 会話 implies an actual back-and-forth of mutual chat; 話 is broader (can mean a story, a single utterance, or a conversation); 対話 is more formal/structured (dialogue, interview). The two-character 漢語 会話 fits naturally with the verbal frame ~を始める ('begin doing X') — perfectly normal in either spoken or written use.