तटाकवनशोभितः adorned with lakes and forests, अयम् this, येन by whom, विप्रानुकम्पया congenial to brahmins, इदम् this, दुष्करम् difficult, कर्म action, कृतम् is done, तस्य his, भ्रातुः brothers, आश्रम: hermitage.

This hermitage surrounded by beautiful lakes and forests belongs to his brother (Sudarsana). Out of sympathy for Agastya, he has accomplished this difficult task.