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\left(\sqrt{6}\right)^{2}-3\sqrt{6}+2\sqrt{6}-6
Apply the distributive property by multiplying each term of \sqrt{6}+2 by each term of \sqrt{6}-3.
6-3\sqrt{6}+2\sqrt{6}-6
The square of \sqrt{6} is 6.
6-\sqrt{6}-6
Combine -3\sqrt{6} and 2\sqrt{6} to get -\sqrt{6}.
-\sqrt{6}
Subtract 6 from 6 to get 0.