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\left(\sqrt{6}\right)^{2}-3\sqrt{6}+7\sqrt{6}-21
Apply the distributive property by multiplying each term of \sqrt{6}+7 by each term of \sqrt{6}-3.
6-3\sqrt{6}+7\sqrt{6}-21
The square of \sqrt{6} is 6.
6+4\sqrt{6}-21
Combine -3\sqrt{6} and 7\sqrt{6} to get 4\sqrt{6}.
-15+4\sqrt{6}
Subtract 21 from 6 to get -15.