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3\times 2-4\sqrt[3]{27}
Calculate \sqrt[4]{16} and get 2.
6-4\sqrt[3]{27}
Multiply 3 and 2 to get 6.
6-4\times 3
Calculate \sqrt[3]{27} and get 3.
6-12
Multiply -4 and 3 to get -12.
-6
Subtract 12 from 6 to get -6.