तृतीया च होश्छन्दसि

Operational rule vidhi

In the छन्दस् (Veda), the object of the verb हु 'to sacrifice' takes the affix of the 3rd case and of the 2nd case as well.

Word by word (padaccheda)

Substitute / term तृतीया prathamā · ekavacanaIndeclinable च avyayaTarget होः ṣaṣṭhī · ekavacanaRight context छन्दसि saptamī · ekavacana

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

तृतीया च होः छन्दसि

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)

होः → तृतीया / छन्दसि

Replace hoḥ with tṛtīyā when chandasi follows. Inherited words (anuvṛtti) may add further conditions.

Commentary

In the छन्दस् (Veda), the object of the verb हु 'to sacrifice' takes the affix of the 3rd case and of the 2nd case as well.
This ordains the third case-affix, and by force of the word च 'and' the second case-affix is also employed as यवाग्वाग्निहोत्रं जुहोति 'he satisfies or pleases Agni with barley-powder,' or यवागुमग्निहोत्रं जुहोति 'he throws barley-powder into the fire as oblation.'

Why do we say 'in the vedas?' In the classical Sanskrit, the accusative only must be used and not the instrumental.

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