Final answer:
Mr. Bingley rents the estate called Nether field in Jane Austen's 'Pride and Prejudice', which is not to be confused with Pemberley, Mr. Darcy's estate, or the other non-related options, Easterday and Northbringer.
Step-by-step explanation:
The mansion that Mr. Bingley is renting in Jane Austen's novel Pride and Prejudice is called Netherfield. This residence plays a significant role in the plot as it is the setting of several key social events, such as balls and dinners, where the characters interact, and the story develops. It differs from the other options provided: Easterday, which is not mentioned in the novel; Pemberley, which is Mr. Darcy's estate: and North bringer, which also is not part of the narrative.