1. **State the problem:** Find the exact value of $\frac{\log_4(6)}{4}$. 2. **Recall logarithm properties:** The expression can be rewritten using the power rule of logarithms: $$\frac{\log_4(6)}{4} = \log_4(6^{\frac{1}{4}})$$ This means taking the fourth root of 6 inside the logarithm. 3. **Rewrite the expression:** $$\log_4(6^{\frac{1}{4}}) = \log_4(\sqrt[4]{6})$$ 4. **Interpretation:** The expression is the logarithm base 4 of the fourth root of 6. This is the exact simplified form. **Final answer:** $$\boxed{\log_4(\sqrt[4]{6})}$$