Explanation:

Biodiversity Heritage Sites (BHS) are areas that are unique, ecologically fragile ecosystems, either terrestrial, coastal and inland waters, or marine areas, having rich biodiversity. They are declared under Section $37$ of the Biological Diversity Act, $2002$. \nOption (A) Gujarat: Gujarat has its own biodiversity-rich areas, but the specific declaration of Amboli as a BHS was not made by the Gujarat government. Therefore, this option is incorrect. \nOption (B) Maharashtra: Amboli is a hill station in the Sindhudurg district of Maharashtra, located in the southern part of the Western Ghats. In $2020$, the Maharashtra government declared a $6.11 \text{ sq km}$ area in Amboli as a biodiversity heritage site. This decision was taken due to the discovery of a new freshwater fish species, 'Schistura hiranyakeshi', in the Hiranyakeshi river, which originates in Amboli. The region is also rich in flora and fauna, including rare and endemic species. Therefore, this option is correct. \nOption (C) Goa: Goa is a neighboring state with its own biodiversity, but Amboli falls within Maharashtra's administrative boundaries, and the declaration was made by the Maharashtra government. Therefore, this option is incorrect. \nOption (D) Karnataka: Karnataka also has significant biodiversity in its part of the Western Ghats, but Amboli is not located in Karnataka, nor was the declaration made by its government. Therefore, this option is incorrect. \nThus, the Maharashtra State Government declared an area at Amboli in the Western Ghats as a biodiversity heritage site.