The correct answer is Option 2: Guru Arjan Dev ... Adi Granth.

Guru Arjan Dev, the fifth Guru of Sikhism, is correctly matched with the compilation of the Adi Granth, also known as the Guru Granth Sahib. The Adi Granth is the central religious scripture of Sikhism, and Guru Arjan Dev played a crucial role in its compilation and installation.

Guru Arjan Dev succeeded his father, Guru Ram Das, as the fifth Guru of the Sikhs in 1581. During his Guruship, Guru Arjan Dev compiled the writings of the previous Gurus, as well as contributions from various other saints and scholars of different religious backgrounds. He organized and arranged these writings into a single volume, known as the Adi Granth, which means "First Book" or "Original Scripture." The Adi Granth contains the teachings, hymns, and compositions of the Gurus, as well as selected writings from other spiritual figures.

Guru Arjan Dev also undertook the task of establishing the Harmandir Sahib, commonly known as the Golden Temple, in Amritsar, Punjab, India. The Adi Granth was first installed at the Harmandir Sahib in 1604, and Guru Arjan Dev placed it on a throne, signifying its status as the eternal Guru of the Sikhs.

It`s important to note that while the other options include other Gurus and significant aspects of Sikh history, they are not correctly matched. Here`s a brief explanation of why the other options are incorrect:

- Option 1: Guru Amar Das is associated with the concept of "Miri and Piri," which represents the Sikh ideals of temporal and spiritual authority. However, "Miri and Piri" is a broader concept that encompasses the teachings of multiple Gurus and is not specific to Guru Amar Das alone.

- Option 3: Guru Ram Das is associated with the establishment of the city of Amritsar and the construction of the Harmandir Sahib. The Dal Khalsa, on the other hand, refers to a military organization formed in the 18th century to resist Mughal rule in Punjab. There is no direct association between Guru Ram Das and the Dal Khalsa.

- Option 4: Guru Gobind Singh, the tenth Guru of Sikhism, is associated with the establishment of the Khalsa, a distinct order of initiated Sikhs. The term "Manji" refers to a system of administrative divisions within the Sikh community, but it is not specifically linked to Guru Gobind Singh.

In conclusion, the correct match is Option 2: Guru Arjan Dev ... Adi Granth, as he compiled and installed the Adi Granth as the central scripture of Sikhism during his Guruship.