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2.4.7 विशिष्टलिङ्गो नदीदेशो-अग्रामाः

द्वन्द्व of words with different genders, indicating rivers, countries but not village (which is related to living beings or social identity) are singular. For example, गङ्गायमुने.

2.4.6 जातिप्राणिनाम्

Non-organism class-indicating द्वन्द्व are singular.

2.4.5 अध्ययनतो-अविप्रकृष्टाख्यानां

Study(dialectics,interpretation)-related द्वन्द्व are singular.

2.4.4 अध्वर्युक्रतुरणपुन्सकं

अध्वर्यु-related यज्ञ-indicating द्वन्द्व are singular. अर्कयज्ञ + अश्वमेधयज्ञ - अर्काश्वमेधं.

2.4.3 अनुवादे चारणानाम्

2.4.3 चरण-indicating words द्वन्द्व  in अनुवाद-sense are  singular. For example, उदगात् कठकालापं.

2.4.2 द्वन्द्वश्च प्राणितूर्यसेनाङ्गानाम्

द्वन्द्व in the case of organs of the body, organs (instruments) and organs (sections) of an army implies singular status as well. For example, पाणिपादं.

2.4.1. द्विगुरेकवचनम्

द्विगु is treated as singular.

2.4

Chapter 2.3 was primarily about cases. Panini provides the rules that govern which cases are tied to the karakas. The world of cases is practically unlimited since they aspire to represent the whole world. The rules aim to connect the semantics of the verbs and words with the roots and suffixes of the language. This is why context (arthha) carries importance in the Chapter 2 rules.
Chapter 2.4 is concerned with number of dvandva. We learn many rules that drive whether dvandva can be treated as singular or not. A remarkable rule is that of small organisms - the collection of which should be considered singular. The rules get into details of what is small and what exceptions might the rule entail.
2.4.18 onwards are rules that decide which tatpurushas would be treated as neuter gender. These are often driven by meaning/sense (2.4.21,2.4.24). The gender is considered 2.4.31 onwards. After a brief commentary on ArdhadhAtuka , the chapter talks about lakars (laT, lan, lin) transforming into luk or otherwise (2.4.40 etc.) - often in the context of certain suffixes.

2.3.73 चतुर्थी चाशिष्यायुष्यमद्रभद्रकुशलसुखार्थहितैः

In आशीर्वाद sense, आयुष्य मद्र भद्र कुशल सुख अर्थ हित may allow चतुर्थी. For example, आयुष्यं देवदत्ताय (देवदत्तस्य).

2.3.72 तुल्यार्थैरतुलोपमाभ्यां तृतीया-अन्यतरस्याम्

In तुल्य sense, तृतीया is implied for indicating the शेषसंबन्ध (except for words तुला and उपमा). For example, देवेन तुल्यः.

2.3.71 कृत्यानां कर्त्तरि वा

कृत्य-suffixed as कर्त्ता have षष्ठी.  There are 7 कृत्य-suffixes - तव्यत् तव्य अनीयर् यत् ण्यत् क्यप् केलिमर. For example, देवस्य कर्तव्यः.

2.3.70 अकेनोर्भविष्यदाधमण्र्योः

Future tense and आधमण्र्य-sense for  इन् suffixes and future tense for अक suffixes prevents षष्ठी. For example, कटं कारको व्रजति (ण्वुल्), ग्रामं गमी (इन् ).

2.3.69 न लोका-अव्ययनिष्ठाखलर्थतृनाम्

No षष्ठी is implied when any of ल उ उक अव्यय निष्ठा खलर्थ तृन् is used. Here,
1. लादेश (ल) includes शतृ शानच् (लट्) कानच् क्वसु (लिट्) कि किन् (स्यत् स्यमन् - लृट्) - For example, ओदनं पचन्.
2. उ implies उकारान्त कृदन्त. For example, कटं चिकीर्षुः.
3. उक implies उक-ending कृदन्त. For example, आगामुकं दैत्यान् घातुकः हरिः.
4. अव्यय implies कृदन्त-अव्यय (in this case). For example, कटं कृत्वा.
5. निष्ठा is defined in 1.1.25. For example, कटं कृतवान्.
6. खल् is defined in 3.3.126. For example, ईषत्करः.
7. तृन् is a suffix defined in 3.2.135. सोमं पवमानः.

2.3.68 अधिकरणवाचिनश्च

अधिकरण-indicating क्त-suffixed कर्त्ता has षष्ठी as well. This reasserts the षष्ठी (from 2.3.65) whenever it's barred.

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2.3.67 क्तस्य च वर्तमाने

क्त-suffix in present tense bears षष्ठी (क्त-suffix is also a कृत्-suffix). For example, राज्ञां मतः (In other tenses the rule is not applied e.g. ग्रामं गतः).

2.3.66 उभयप्राप्तो कर्मणि

When कर्त्ता and कर्म are associated with कृत्-suffix then षष्ठी is implied (example?).

However, with अक and अ-ending कृत्-suffixes, षष्ठी is implied for both कर्त्ता and कर्म. For example, चिकीर्षा देवस्य कटस्य.

Some experts indicate षष्ठी for कर्त्ता and तृतीया/षष्ठी for कर्म - in the context of (non-अक and non-अ) कृदन्तs. For example, विचित्रा जगतः कृतिः हरेः / हरिणा.

2.3.65 कर्तृकर्मणोः कृति

कृत्-suffix ending words combining have षष्ठी in कर्त्ता or कर्म. For example, कालिदासस्य कृतिः. Note that it is only in case of कृत् that the rule is applied - भुक्तपूर्वी उदनं doesn't have षष्ठी.

2.3.64 कृत्वो-अर्थप्रयोगे काले-अधिकरणे

कृत्वसुच् etc. suffix, time-indicating अधिकरण bears षष्ठी. For example, In पञ्चकृत्वो अह्नो भुङ्क्ते, अह्नो is षष्ठी.  षष्ठी is not implied in the absence of कृत्वसुच् or in the absence of time-indicating अधिकरण case  - for example, अह्ने शेते (सप्तमी - sleeps in the day).

2.3.63 यजेश्च करणे

बहुलता results in करण for यज्. For example, घृतस्य यजते (even though ghee is करण).

2.3.62 चतुत्यर्थे बहुलं छन्दसि

In vedic hymns, the sense of चतुर्थी may bear षष्ठी.