बहुपूगगणसंघस्य तिथुक्

Operational rule vidhi

When डट् follows, तिथुक् is the augment of the words 1. बहु 2. पूग 3. गण and 4. सङ्गघ.

Word by word (padaccheda)

Target बहु- पूग- गण- सङ्घस्य ṣaṣṭhī · ekavacanaSubstitute / term तिथुक् prathamā · ekavacana

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.

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Full reading

बहु-पूग-गण-सङ्घस्य तिथुक्

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)

बहु- पूग- गण- सङ्घस्य → तिथुक्

Replace bahu-pūga-gaṇa-saṅghasya with tithuk. Inherited words (anuvṛtti) may add further conditions.

Commentary

When डट् follows, तिथुक् is the augment of the words 1. बहु 2. पूग 3. गण and 4. सङ्गघ।
The word डटि is understood here also. The words पूग and संघ are not Numerals; they take the affix डट् by virtue of this sutra. Thus बहूनां पूरणो = बहुतिथः, पूगतिथः, गणतिथः, and संघतिथः ॥

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