1. **State the problem:** We are given the equation $\log_x y + 6 \log_x (2^3) = 3$ and need to express $y$ in terms of $x$. 2. **Rewrite powers inside the logarithm:** Note that $2^3 = 8$, so the equation becomes: $$\log_x y + 6 \log_x 8 = 3$$ 3. **Apply the logarithm multiplication rule:** Use the property $a \log_b c = \log_b c^a$ to combine terms: $$\log_x y + \log_x 8^6 = 3$$ 4. **Simplify powers:** Calculate $8^6$: $$8^6 = (2^3)^6 = 2^{18}$$ So the equation is: $$\log_x y + \log_x 2^{18} = 3$$ 5. **Combine logarithms:** Using the property $\log_b m + \log_b n = \log_b (mn)$: $$\log_x(y \cdot 2^{18}) = 3$$ 6. **Convert logarithmic equation to exponential form:** Recall $\log_x M = N \implies M = x^N$, so: $$y \cdot 2^{18} = x^3$$ 7. **Isolate $y$:** $$y = \frac{x^3}{2^{18}}$$ **Final answer:** $$\boxed{y = \frac{x^3}{2^{18}}}$$