To estimate the value of \(6 \times 2 - \sqrt{6}\), we first calculate \(6 \times 2\):
\[ 6 \times 2 = 12 \]
Next, we need the value of \(\sqrt{6}\). Since \(6\) is between \(2^2 = 4\) and \(3^2 = 9\), we know that \(\sqrt{6}\) is between \(2\) and \(3\). A more precise approximation for \(\sqrt{6}\) is approximately \(2.45\).
Now we can subtract this from \(12\):
\[ 12 - \sqrt{6} \approx 12 - 2.45 = 9.55 \]
Considering the options provided, the best estimate for \(6 \times 2 - \sqrt{6}\) is:
- 9.8
Thus, the best estimate is \(\mathbf{9.8}\).