1. **State the problem:** We are given the equation $3x = 2y + 3$ and asked to find the expression $\frac{8^x}{4^y}$. 2. **Rewrite the bases:** Recall that $8 = 2^3$ and $4 = 2^2$, so we can rewrite the expression as: $$\frac{8^x}{4^y} = \frac{(2^3)^x}{(2^2)^y} = \frac{2^{3x}}{2^{2y}}$$ 3. **Use the quotient rule for exponents:** $$\frac{2^{3x}}{2^{2y}} = 2^{3x - 2y}$$ 4. **Express $3x - 2y$ using the given equation:** From $3x = 2y + 3$, subtract $2y$ from both sides: $$3x - 2y = 3$$ 5. **Substitute back:** $$2^{3x - 2y} = 2^3$$ 6. **Calculate the final value:** $$2^3 = 8$$ **Final answer:** $$\frac{8^x}{4^y} = 8$$