दूरान्तिकार्थैः षष्ठ्यन्यतरस्याम्

Operational rule vidhi

When in conjunction with words having the sense of दूर 'distant' and अन्तिक 'near', the 6th-Case-affix is optionally used.

Word by word (padaccheda)

With / by दूरा- अन्तिक- अर्थैः tṛtīyā · bahuvacanaSubstitute / term षष्ठी prathamā · ekavacanaRight context अन्यतरस्याम् saptamī · ekavacana

With / by Tṛtīyā (3rd case): accompaniment or means.
Substitute / term Prathamā (1st case): in operational rules, the substitute or the thing introduced; in definitions, the term or its referent.
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").

Full reading

दूरा-अन्तिक-अर्थैः षष्ठी अन्यतरस्याम्

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

Commentary

When in conjunction with words having the sense of दूर 'distant' and अन्तिक 'near', the 6th-Case-affix is optionally used.
Ex. ग्रामाद् ग्रामस्य वा वनं दूरं विप्रकृष्टं, अन्तिकं, अभ्याशं, निकटं समीपं वा 'the forest is distant or near or to the village.'

The force of the word अन्यतरस्यां is to indicate that the 5th case-affix employed in the alternative, would have run into this sutra, had we not used 'anyatarasyam.'

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