अजिनान्तस्योत्तरपदलोपश्च

Operational rule vidhi

The affix कन् comes in the sense of compassion, after a man-name ending in अजिन and this second member is elided before the affix.

Word by word (padaccheda)

Target अजिन- अन्तस्य ṣaṣṭhī · ekavacanaSubstitute / term उत्तरपदलोपः prathamā · ekavacanaIndeclinable च avyaya

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.
Indeclinable An avyaya such as च "and", वा "optionally", न "not".

Dotted words are technical terms. Hover or tap one to see its card.

Full reading

अजिन-अन्तस्य उत्तरपदलोपः च

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)

अजिन- अन्तस्य → उत्तरपदलोपः

Replace ajina-antasya with uttarapadalopaḥ. Inherited words (anuvṛtti) may add further conditions.

Commentary

The affix कन् comes in the sense of compassion, after a man-name ending in अजिन and this second member is elided before the affix.
The words कन् and मनुष्यनाम्नः are understood in this sutra. Thus व्याघ्रकः from व्याघ्राजिनः, and सिंहकः from सिंहाजिनः ॥ Vyaghrajina and Sinhajina are names of men.

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