To multiply \( \sqrt{6}(\sqrt{2} - 2\sqrt{7}) \), we'll distribute \( \sqrt{6} \) to each term inside the parentheses:
\[ \sqrt{6} \cdot \sqrt{2} - \sqrt{6} \cdot 2\sqrt{7} \]
Now, we can simplify each term:
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For the first term: \[ \sqrt{6} \cdot \sqrt{2} = \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3} \]
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For the second term: \[ \sqrt{6} \cdot 2\sqrt{7} = 2\sqrt{42} \]
Putting it all together, we have:
\[ 2\sqrt{3} - 2\sqrt{42} \]
We can factor out the common factor of 2:
\[ 2(\sqrt{3} - \sqrt{42}) \]
Therefore, the simplified expression is:
\[ \boxed{2(\sqrt{3} - \sqrt{42})} \]
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