This is plate 21 from James Baillie Fraser's 'Views of Calcutta and its Environs'. Fraser (1783-1856) arrived in Calcutta in 1814 and in six years produced these animated sketches of the busy city. The collection included two views at Barrackpore.
This one shows the view from Barrackpore Park across the river to Serampore or Srirampur, a Dutch settlement on the opposite bank laid out in the 'English Style' by Marquess Wellesley. In Bishop Heber's words: "The Governor General has a very pretty country residence at Barrackpore ... offering ... beautiful a display of turf, tree and flowering shrub..." Its extensive grounds contained a theatre, an aviary and a menagerie. It was also possible to ride around the park on the back of an elephant.
Source: British Library (bl.uk)