सा कैकयी that Kaikeyi, तस्य रामस्य such Rama's, तत् वाक्यम् those words, श्रुत्वा having heard, हृष्टा happy, प्रस्थानम् departure, श्रद्धधाना believing, राघवम् to Rama, त्वरयामास hastened (him).

Kaikeyi, happy to hear the words of the son of the Raghus as she was convinced that his departure (to the forest) was certain, hastened him (to set out).