。
She had to choose her words carefully.
Literal
She [topic-は] her own words [object-を] carefully choose [must-なければならなかった].
言葉を選ぶ ('to choose one's words') is a stock collocation for being deliberate in how one speaks — picking the right wording to avoid offense or misunderstanding. 慎重に ('carefully, prudently, cautiously') is the adverbial form of the na-adjective 慎重. ~なければならない is the standard obligation pattern ('must / have to'); past ~なければならなかった makes it a past obligation. Belongs to the register of delicate or high-stakes conversation — diplomatic, sensitive, or charged.