。。
You look tired. Shall I drive?
Literal
Tired appearance [right-ね]. I [subject-が] steering-wheel let's-grip [question-か].
疲れた様子だね observes the person's appearance. ハンドルを握る means 'to grip the steering wheel' = 'to drive.' ~ろうか uses the volitional + か to offer: 'shall I?' A natural, caring exchange.