नृपतेः सुतः king's son, दीनः depressed, सम्भ्रान्तः perplexed, न कच्चित् not indeed, कार्येषु at work, न च मुह्यति is not spoiling, पुरुषकार्याणि the actions of men of achievement, कच्चित् कुरुते surely he is doing I trust

"I suppose prince Rama is not too depressed or perplexed to attend to his work. He will (perhaps) be doing the duties expected of a manly person.