。
She suggested I cancel the meeting.
Literal
She [topic-は] me [to-に] meeting [object-を] cancel-do [how about-てはどうか] [quotative-と] proposed.
~てはどうか ('how about doing X? / how would it be if you did X?') is a soft suggestion frame — literally 'as for doing X, how is it?' The rhetorical question form invites consideration rather than directing — a typical Japanese softening strategy for proposing actions. 提案する ('to propose, to suggest') is a more formal verb than 言う or 勧める, common in business and formal contexts. The combination — soft suggestion frame + formal proposing verb — fits naturally in workplace situations.