Solve for \( y \) in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. \[ 3^{-6 y}=12 \]

Solve the equation \( 3^{-6y}=12 \). Solve the equation by following steps: - step0: Solve for \(y\): \(3^{-6y}=12\) - step1: Take the logarithm of both sides: \(\log_{3}{\left(3^{-6y}\right)}=\log_{3}{\left(12\right)}\) - step2: Evaluate the logarithm: \(-6y=\log_{3}{\left(12\right)}\) - step3: Change the signs: \(6y=-\log_{3}{\left(12\right)}\) - step4: Divide both sides: \(\frac{6y}{6}=\frac{-\log_{3}{\left(12\right)}}{6}\) - step5: Divide the numbers: \(y=-\frac{\log_{3}{\left(12\right)}}{6}\) - step6: Simplify: \(y=-\frac{1+2\log_{3}{\left(2\right)}}{6}\) Round the number \\( -\frac{1+2\log_{3}{(2)}}{6} \\) to hundredth. Round the number by following steps: - step0: Round \(-\frac{1+2\log_{3}{(2)}}{6}\) to \(2\) decimal places using standard rounding method: \(-\frac{1+2\log_{3}{(2)}}{6}\) - step1: Evaluate: \(-\frac{1+2\log_{3}{\left(2\right)}}{6}\) - step2: Rewrite in decimal: \(-0.376977\) - step3: Round \(-0.376977\) to \(2\) decimal places using standard rounding method\(:\) \(-0.38\) The solution to the equation \(3^{-6y}=12\) is \(y \approx -0.38\).