Step 1: Understanding the Concept:
The 12 houses of a horoscope are grouped based on their spatial orientation relative to the Ascendant. These groups—Kēndra, Paṇaphara, and Apōklima—describe the inherent strength and 'action-potential' of planets placed in those houses. Trikōṇa is a separate grouping based on the trinal relationship.
Step 2: Detailed Explanation:
1. 1, 4, 7, 10 (A): These are the 'Angular' houses, known as Kēndra-sthānas (IV). They are the strongest houses. Planets here are highly active and manifest results externally. They are the 'Viṣṇu-Sthānas'. (A-IV)
2. 2, 5, 8, 11 (B): These are the 'Succedent' houses, known as Paṇaphara-sthānas (I). 'Pana' means money or weight. These houses are medium in strength. Planets here give results in the middle part of life. (B-I)
3. 3, 6, 9, 12 (C): These are the 'Cadent' houses, known as Apōklima-sthānas (III). They are considered the weakest in terms of direct manifest strength. (C-III)
4. 1, 5, 9 (D): These are the 'Trinal' houses, known as Trikōṇa-sthānas (II). These are the most auspicious houses, representing divine grace and intelligence. They are 'Lakṣmī-Sthānas'. (D-II)
This classification is foundational for 'Bhāva-bala' (house strength). A planet in a Kēndra has $100\%$ strength to act, in a Paṇaphara $50\%$, and in an Apōklima $25\%$. Note that the 1st house (Lagna) is uniquely both a Kēndra and a Trikōṇa, making it the most vital house of all.
Step 3: Final Answer:
The correct match is A-IV, B-I, C-III, D-II.