Four.
1940 Nominated Oscar Best Director for: Stagecoach (1939)
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Brokeback Mountain was nominated for 6 Oscars. It won 3 of them: Best Directing Best Score Best Adapted Screenplay
It did not win any Oscars.
It was nominated for one (visual effects) but didn't win any.
The 1996 film version of John Grisham's novel was not nominated for any Academy Awards.
No.