Every 2 ounces of butter is enough to cover 1 cup of baking mix, so the chef's remaining 4 ounces of butter will be enough to cover 4/2 = <<4/2=2>>2 cups of baking mix.
This leaves 6 - 2 = <<6-2=4>>4 cups of baking mix that will require the use of coconut oil as a substitute.
Since each cup of baking mix requires 2 ounces of coconut oil, these 4 cups will require a total of 4*2 = <<4*2=8>>8 ounces of coconut oil.
#### 8