Canto 2 -
Ayodhyā-kāṇḍa
Chapter 24: Rāma Instructs Kausalyā
Text 2.24.17
इमानि तु महारण्ये विहृत्य नव पञ्च च।
वर्षाणि परमप्रीतः स्थास्यामि वचने तव॥
imāni tu mahāraṇye vihṛtya nava pañca ca
varṣāṇi parama-prītaḥ sthāsyāmi vacane tava
imāni tu = for these [upcoming]; mahā-araṇye = in the great forest; vihṛtya = after sporting; nava = nine; pañca = five; ca = and; varṣāṇi = years; parama-prītaḥ = in great happiness; sthāsyāmi = I will abide; vacane = by words; tava = your.
After sporting in the great forest for these [upcoming] nine and five years in great happiness, I will abide by your words.
First of all, Rāma wanted to carry out the instruction of His father. That is pointed out here.
Vihṛtya (“after sporting”) indicates that Rāma would be free from distress.