2log\(_{3}\) 6 + log\(_{3}\) 12 - log\(_{3}\) 16

= \(\log_3 6^2 + \log_3 12 - \log_3 16\)

= \(\log_{3} (\frac{36 \times 12}{16})\)

= \(\log_{3} (27)\)

= \(\log_{3} 3^3\)

= \(3 \log_{3} 3\)

= 3