Valmiki Ramayana Ayodhya Kanda Sarga 19 Shloka 12
Original Shlokaसा हृष्टा तस्य तद्वाक्यं श्रुत्वा रामस्य कैकयी। प्रस्थानं श्रद्धधाना हि त्वरयामास राघवम्।।2.19.12।।
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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).