When Ráma thus had made reply Kaikeyí’s heart with joy beat high. She, trusting to the pledge she held, The youth’s departure thus impelled: “’Tis well. Be messengers despatched On coursers ne’er for fleetness matched, To seek my father’s home and lead My Bharat back with all their speed.

In plain words: Kaikeyi is overjoyed at Rama's answer. Relying on the promise the king made her, she agrees to send the fastest messengers to bring Bharata home.