$\begin{aligned}
A & = 2\ln 4 + \ln 27 - 4\ln 18 + 4\ln \sqrt{6 } - \ln \dfrac{9}{16} \\
& = 2\ln 2^2 + \ln 3^3 - 4\ln(2\times3^2) + 4\ln\bigl((2\times3)^{\frac{1}{2}}\bigr) - (\ln 3^2 - \ln 2^4)\\
& = 4\ln 2 + 3\ln 3 - 4(\ln 2 + 2\ln 3) + 4\times\dfrac{1}{2}(\ln 2 + \ln 3) - 2\ln 3 + 4\ln 2 \\
& = 4\ln 2 + 3\ln 3 - 4\ln 2 - 8\ln 3 + 2\ln 2 + 2\ln 3 - 2\ln 3 + 4\ln 2 \\
 & = 6\ln 2 - 5\ln 3.
\end{aligned}$
