1. **State the problem:** We have a rectangular garden with a perimeter of 64 meters. The length is 8 meters longer than the width. We need to find the length and width. 2. **Formula for perimeter of a rectangle:** $$P = 2(L + W)$$ where $L$ is length and $W$ is width. 3. **Express length in terms of width:** Given $L = W + 8$. 4. **Substitute into perimeter formula:** $$64 = 2((W + 8) + W)$$ 5. **Simplify inside the parentheses:** $$64 = 2(2W + 8)$$ 6. **Distribute 2:** $$64 = 4W + 16$$ 7. **Isolate $W$:** $$64 - 16 = 4W$$ $$48 = 4W$$ 8. **Solve for $W$:** $$W = \frac{48}{4} = 12$$ 9. **Find $L$ using $L = W + 8$:** $$L = 12 + 8 = 20$$ **Final answer:** The width is 12 meters and the length is 20 meters.