Which period is specified as the time when the Kangra style initiated a local school of Hindu book illumination in Kashmir?

1846–1885

The correct answer is option 4: 1846–1885.

The Kangra School came to fore in the 1780s while the offshoots of the Basohli style emerged and continued in centres such as Chamba, Kullu, Nurpur, Mankot, Jasrota, Mandi, Bilaspur, Jammu and others with some of their specific characteristics. In Kashmir (1846–1885), the Kangra style initiated a local school of Hindu book illumination. The Sikhs employed other Kangra painters eventually.