1. **State the problem:** Simplify the expression $\log_2 \sqrt[4]{p^2 y^{12}}$. 2. **Recall the formula:** The logarithm of a root can be rewritten using the power rule: $\log_b (x^r) = r \log_b x$. 3. **Rewrite the root as a power:** $$\sqrt[4]{p^2 y^{12}} = (p^2 y^{12})^{\frac{1}{4}}$$ 4. **Apply the power to each factor inside the parentheses:** $$(p^2)^{\frac{1}{4}} (y^{12})^{\frac{1}{4}} = p^{\frac{2}{4}} y^{\frac{12}{4}} = p^{\frac{1}{2}} y^3$$ 5. **Rewrite the logarithm using the product rule:** $$\log_2 (p^{\frac{1}{2}} y^3) = \log_2 p^{\frac{1}{2}} + \log_2 y^3$$ 6. **Use the power rule for logarithms:** $$\frac{1}{2} \log_2 p + 3 \log_2 y$$ **Final answer:** $$\boxed{\frac{1}{2} \log_2 p + 3 \log_2 y}$$