Answer
$\displaystyle \ln\frac{(x+6)^{4}}{x^{3}}$
Work Step by Step
$ 4\ln(x+6)-3\ln x=\quad $...apply the Power Rule: $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$
$=\ln(x+6)^{4}-\ln x^{3}\quad $...apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$
$=\displaystyle \ln\frac{(x+6)^{4}}{x^{3}}$