अन्वयः

स: दशरथ: राजा that king Dasaratha, मात्रा by mother, पित्रा दशरथेन च by father Dasaratha (by himself), कृतस्वस्त्ययनम् giving farewell by recitation of mantras for securing prosperity and averting evils, पुरोधसा वसिष्ठेन by priest Vasishta, मङ्गलै: by auspicious, अभिमन्त्रितम् making sacred by recitation of special mantras, प्रियम् पुत्रम् affectionate son, मूर्ध्नि on the forehead, उपाघ्राय having kissed, सुप्रीतेन with a pleased, अन्तरात्मना heart, कुशिकपुत्राय for kusika's son, ददौ delivered Rama (to the care of Viswamitra).

M N Dutt

And when the auspicious rites had been performed by both Rāma's father and mother, and when the priest Vasiştha had uttered mantras, king Dasaratha, smelling his son's crown, with a glad heart, made him over to the descendant of Kusika.

Summary

Rama was given farewell by his parents with recitation of mantras (for securing prosperity and averting evils). Priest Vasishta sanctified him with mantras Dasaratha kissed his son on the forehead and delivered him to the care of Viswamitra, with a heart full of cheer.

पदच्छेदः

कृतस्वस्त्ययनं	कृत (√कृ + क्त)–स्वस्त्ययन (२.१)
मात्रा	मातृ (३.१)
पित्रा	पितृ (३.१)
दशरथेन	दशरथ (३.१)
च	च (अव्ययः)
पुरोधसा	पुरोधस् (३.१)
वसिष्ठेन	वसिष्ठ (३.१)
मङ्गलैर्	मङ्गल (३.३)
अभिमन्त्रितम्	अभिमन्त्रित (√अभि-मन्त्रय् + क्त, २.१)

छन्दः

अनुष्टुप् [८]

छन्दोविश्लेषणम्

१	२	३	४	५	६	७	८
कृ	त	स्व	स्त्य	य	नं	मा	त्रा
पि	त्रा	द	श	र	थे	न	च
पु	रो	ध	सा	व	सि	ष्ठे	न
म	ङ्ग	लै	र	भि	म	न्त्रि	तम्