Explanation:

This question asks us to identify an example of 'Vyanjan Sandhi' (Consonant Sandhi) from the given options. Sandhi refers to the euphonic conjunction of sounds, and in Hindi/Sanskrit grammar, it's broadly categorized into Swar Sandhi (Vowel Sandhi), Vyanjan Sandhi (Consonant Sandhi), and Visarga Sandhi (Visarga Conjunction). **Vyanjan Sandhi** occurs when a consonant is followed by either a vowel or another consonant, leading to a change in one or both sounds. **Swar Sandhi** occurs when two vowels combine, resulting in a change in the vowels. Let's break down each option to determine its Sandhi type: **Option (A): सतीश (Satish)** This word is typically formed by combining 'सती' (Sati, a name) + 'ईश' (Ish, lord). Here, the vowel 'ई' (ī) from 'सती' combines with the vowel 'ई' (ī) from 'ईश'. According to the Dirgha Swar Sandhi rule, 'ई + ई = ई' (a long vowel is formed when two similar vowels combine). Thus, 'सती + ईश = सतीश'. This is an example of **Swar Sandhi**, not Vyanjan Sandhi. **Option (B): कपीश (Kapeesh)** This word is formed by combining 'कपि' (kapi, monkey) + 'ईश' (Ish, lord). Here, the vowel 'इ' (i) from 'कपि' combines with the vowel 'ई' (ī) from 'ईश'. According to the Dirgha Swar Sandhi rule, 'इ + ई = ई'. Thus, 'कपि + ईश = कपीश'. This is an example of **Swar Sandhi**, not Vyanjan Sandhi. **Option (C): जानकीश (Janakish)** This word is formed by combining 'जानकी' (Janaki, another name for Sita) + 'ईश' (Ish, lord). Here, the vowel 'ई' (ī) from 'जानकी' combines with the vowel 'ई' (ī) from 'ईश'. According to the Dirgha Swar Sandhi rule, 'ई + ई = ई'. Thus, 'जानकी + ईश = जानकीश'. This is an example of **Swar Sandhi**, not Vyanjan Sandhi. **Option (D): वागीश (Vagish)** This word is formed by combining 'वाक्' (vāka, speech) + 'ईश' (Ish, lord). Here, the consonant 'क्' (k) from 'वाक्' is followed by the vowel 'ई' (ī) from 'ईश'. According to a fundamental rule of Vyanjan Sandhi, if a pure consonant (like 'क्', 'च्', 'ट्', 'त्', 'प्' – the first letter of a Varg/class) is followed by a vowel or a soft consonant (third, fourth, fifth letters of a Varg, or 'य', 'र', 'ल', 'व', 'ह'), the first consonant changes into the third letter of its own Varg. In this case, 'क्' (first letter of 'क' Varg) changes to 'ग्' (third letter of 'क' Varg). Then, this 'ग्' combines with the following vowel 'ई' to form 'गी'. Thus, 'वाक् + ईश = वागीश'. This is a clear and classic example of **Vyanjan Sandhi**. **Conclusion:** After analyzing the Sandhi rules for each word, it is evident that 'वागीश' is the only example of Vyanjan Sandhi, where a consonant ('क्') changes due to its conjunction with a vowel ('ई'). The other options are all examples of Swar Sandhi. Therefore, option (D) is the correct answer.