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To divide \( 8\sqrt{6} \) by \( 2 \), we perform the division as follows:
\[
\frac{8\sqrt{6}}{2} = 4\sqrt{6}
\]
So the exact answer is \( 4\sqrt{6} \).
It is neither \( 4\sqrt{6}\sqrt{3} \) nor \( 8\sqrt{3} \). Therefore, the correct answer is \( 4\sqrt{6} \).