आयुक्तकुशलाभ्यां चासेवायाम्

Operational rule vidhi

In conjunction with the words आयुक्त 'engaged', and कुशल 'skilful', when meaning entire absorption in an engagement, the 6th and the 7th case-affixes are used after a word.

Word by word (padaccheda)

With / by आयुक्त- कुशलाभ्याम् tṛtīyā · dvivacanaIndeclinable च avyayaRight context आसेवायाम् saptamī · ekavacana

With / by Tṛtīyā (3rd case): accompaniment or means.
Indeclinable An avyaya such as च "and", वा "optionally", न "not".
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

आयुक्त-कुशलाभ्याम् च आसेवायाम्

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

Commentary

In conjunction with the words आयुक्त 'engaged', and कुशल 'skilful', when meaning entire absorption in an engagement, the 6th and the 7th case-affixes are used after a word.
Ex. आयुक्तः कुशलो वा कटकरणे कटकरणस्य वा 'deeply absorbed in mat-making.'

When not meaning 'deeply absorbed,' the construction is different; as आयुक्तो गौ शकटे 'the cow is slightly yoked to the cart.' Here the seventh case-affix only is employed.

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