、。
The travel agent suggested taking traveler's checks.
Literal
Travel-agency [possessive-の] person [topic-は], traveler-use checks [object-を] take-go [how-about-てはどうか] [quotative-と] suggested.
~てはどうか (how about doing X?) is a suggestion pattern — literally 'how would it be if you did X?' 持っていく (take with you) combines 持つ (hold) + いく (go) = 'take along.' 提案する (to suggest/propose) is a formal verb for making suggestions.