धः कर्मणि ष्ट्रन्

Operational rule vidhi

The affix ष्ट्रन् comes, in denoting the object after the verb धा 'to feed'.

Word by word (padaccheda)

Target धः ṣaṣṭhī · ekavacanaRight context कर्मणि saptamī · ekavacanaSubstitute / term ट्र prathamā · 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").
Substitute / term Prathamā (1st case): in operational rules, the substitute or the thing introduced; in definitions, the term or its referent.

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Full reading

धः कर्मणि ष्ट्रन्

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

As a rewrite rule (sketch from case endings)

धः → ष्ट्रन् / कर्मणि

Replace dhaḥ with ṣṭran when karmaṇi follows. Inherited words (anuvṛtti) may add further conditions.

Commentary

The affix ष्ट्रन् comes, in denoting the object after the verb धा 'to feed'.
The indicatory ष denotes that the feminine is formed by ङीप् (ई) affix. As धात्री 'a nurse whom the children suck (dhayanti)'; and 'Amalaki fruit which holds (dadhati) all medicinal properties'.

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