अश्वस्यैकाहगमः

Operational rule vidhi

The affix खञ् comes in the sense of 'what is travelled over or traversed in one day' after the word अश्व being in the Genitive 6th-Case in construction.

Word by word (padaccheda)

Target अश्वस्य ṣaṣṭhī · ekavacanaSubstitute / term एकाहगमः prathamā · ekavacana

Target Ṣaṣṭhī (6th case): names what gets replaced, "in place of X" (1.1.49 षष्ठी स्थानेयोगा).
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

अश्वस्य एकाहगमः

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)

अश्वस्य → एकाहगमः

Replace aśvasya with ekāhagamaḥ. Inherited words (anuvṛtti) may add further conditions.

Commentary

The affix खञ् comes in the sense of 'what is travelled over or traversed in one day' after the word अश्व being in the Genitive 6th-Case in construction.
The word अश्वस्थ being in the sixth case shows the construction it should have before the affix. The एकाहगमः means एकाहेन गम्यते i.e. what is or can be gone over in one day. Thus अश्वस्यैकाहगमोऽध्वा = आश्वीनः, as आश्वीनानि शतं पतित्वा = यावन्ति योजनान्येकाहेनाश्वेन गम्यते तावतां शतं गत्वा ॥ सहस्राश्वीने वा इतः स्वर्गो लोकः ॥

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