Answer
$\log_{4}\sqrt[3]{\frac{x}{y}}$
Work Step by Step
$\displaystyle \frac{1}{3}(\log_{4}x-\log_{4}y)=\quad $...apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$
$=\displaystyle \frac{1}{3}\cdot\log_{4}(\frac{x}{y}) \quad $...apply the Product Rule: $\quad \log_{b}(MN)=\log_{b}\mathrm{M}+\log_{b}\mathrm{N}$
$=\displaystyle \log_{4}(\frac{x}{y})^{1/3}=\log_{4}\sqrt[3]{\frac{x}{y}}$