During the "golden age" of Hollywood, The Big Eight referred to the eight major Hollywood movie studios. Since then, the number of major studios has fluctuated with bankruptcies -- RKO Radio Pictures, mergers -- United Artists and the 'promotion' of what was previously a 'minor' studio, e.g. The Walt Disney Company. The demotion of MGM leaves a current Big Six.
Big Eight is sometimes used to refer to the eight corporations that own the Big Ten, the ten major Hollywood movie studios.
References
Big Eight (film studios) Wikipedia(Text) CC BY-SA