Understanding the Question: The question asks to identify the specific rule of phonetic combination (Sandhi) that occurs when the words Hima and Ālaya join to form Himālaya.
Key Concepts and Approach: When two similar vowels (Savarṇa) meet, they merge into a single long vowel (Dīrgha). The rule in Pāṇini's grammar is "Akaḥ savarṇe dīrghaḥ" (6.1.101).
Detailed Solution:
Step 1: Splitting the Compound. The word Himālaya is composed of Hima (Snow) + Ālaya (Abode).
Step 2: Analyzing the Junction. The final letter of Hima is 'a' (short). The initial letter of Ālaya is 'ā' (long).
\[ a + \bar{a} = \bar{a} \]
Step 3: Identifying the Rule. Since 'a' and 'ā' are "Savarna" (similar/homogeneous) vowels, and they result in a "Dirgha" (long) vowel 'ā', the rule is Savarṇa Dīrgha Sandhi.
Step 4: Correction of previous data. Note that Yan Sandhi occurs when $i, u, \text{or } ṛ$ change to $y, v, \text{or } r$. That is not the case here.
Conclusion: The correct rule is Savarṇa Dīrgha Sandhi.