1. **State the problem:** Given the equation $\log_x y + 6 \log_x (2^3) = 3$, express $y$ in terms of $x$. 2. **Rewrite the logarithmic terms:** Note that $2^3 = 8$, so $6 \log_x (2^3) = 6 \log_x 8$. 3. **Use the logarithm power rule:** $6 \log_x 8 = \log_x 8^6$ because $a \log_b c = \log_b c^a$. 4. **Simplify the expression:** The equation becomes $\log_x y + \log_x 8^6 = 3$. 5. **Combine the logarithms on the left:** $\log_x (y \cdot 8^6) = 3$ because $\log_x a + \log_x b = \log_x (ab)$. 6. **Convert the log equation to exponential form:** $y \cdot 8^6 = x^3$; this follows from $\log_x A = B \Rightarrow A = x^B$. 7. **Solve for $y$:** $y = \frac{x^3}{8^6}$. 8. **Express $8^6$ in terms of powers:** Since $8 = 2^3$, $8^6 = (2^3)^6 = 2^{18}$. 9. **Final answer:** $\boxed{y = \frac{x^3}{2^{18}}}$.