"The Big Six" are the six main film production companies, they are:
Warner Brothers, Paramount, Columbia, Universal, 20th Century Fox, Walt Disney/Touchstone.
They are all based in or around Hollywood, USA and have been active since about the 1930's in the "Golden Age" of Hollywood.
20th Century Fox is currently owned by News Corporation which is owned by Australian-American businessman Rupert Murdoch, the original company was founded in 1935 when two companies merged, Fox Film Corporation and Twentieth Century Films.
The founder of the company was Jewish-Hungarian immigrant to the United States William Fox