नद्याः शेषस्यान्यतरस्याम्

Operational rule vidhi

In all the remaining feminine words called नदी -- यू स्त्र्याख्यौ नदी (1.4.3) and नेयङुवङ्स्थानावस्त्री (1.4.4), the substitution of short vowel under the preceding circumstances is optional.

Word by word (padaccheda)

Target नद्याः ṣaṣṭhī · ekavacanaTarget शेषस्य ṣaṣṭhī · ekavacanaRight context अन्यतरस्याम् saptamī · ekavacana

Target Ṣaṣṭhī (6th case): names what gets replaced, "in place of X" (1.1.49 षष्ठी स्थानेयोगा).
Right context Saptamī (7th case): "when X follows", the operation applies to what precedes (1.1.66 तस्मिन्निति निर्दिष्टे पूर्वस्य). Also a condition or domain ("in the sense of").

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Full reading

नद्याः शेषस्य अन्यतरस्याम्

Pāṇini leaves out words that carry over from earlier sūtras. Expand to see the rule as a reader actually understands it.

Commentary

In all the remaining feminine words called नदी -- यू स्त्र्याख्यौ नदी 1.4.3 and नेयङुवङ्स्थानावस्त्री 1.4.4, the substitution of short vowel under the preceding circumstances is optional.
What are the शेष or the remnants? Those feminines which are not formed by long ई (ङी), and are called Nadi; and those feminines which end in long ई but consist of one syllable. Thus ब्रह्मबन्धूतरा or ब्रह्मबन्धुतरा वीरबन्धूतरा or वीरबन्धुतरा, स्त्रितरा or स्त्रीतरा, स्त्रितमा or स्त्रीतमा ॥

Vart:- Nadi words formed by कृत् affixes are excepted: as लक्ष्मीतरा, तन्त्रीतरा formed by the Unadi affix ई (Unadi III.I58.160)

Śrīśa Chandra Vasu, The Ashtadhyayi of Panini (1897), via ashtadhyayi.com.