。
Why don't you give baseball a try?
Literal
Baseball [obj-を] do-[try-てみる]-[how-about-てはどうですか].
Stacks two auxiliaries: やってみる ('try doing') + ~てはどうですか ('how about doing X?'). The effect is a gentle, casual suggestion — 'try X-ing, how about that?' やる is the casual synonym of する ('do').