Bhashya
अथैनं मात्रे प्रदाय स्वाङ्कस्थम्, स्तनं प्रयच्छति 'यस्तेस्तनः' इत्यादिमन्त्रेण ॥
In plain words
He hands the child to his mother, who settles him in her lap and offers her breast, speaking the mantra that begins 'that breast of yours...'.
Close to the Sanskrit
Then, having given him over to the mother, [the child now] resting in her own lap, she gives [him] the breast, by the mantra beginning 'that breast of yours' [and so on].