का पथ्यक्षयोः

Operational rule vidhi

का is the substitute of कु before पथिन् and अक्ष.

Word by word (padaccheda)

Word का Right context पथि- अक्षयोः saptamī · dvivacana

Word Case not marked in the source data.
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").

का पथि-अक्षयोः

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

का is the substitute of कु before पथिन् and अक्ष।
Thus कापथः and काक्षः ॥

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