1. **State the problem:** We need to find the length $x$ of a rectangular window with width 4 feet such that its area is more than 12 square feet but not more than 24 square feet. 2. **Write the formula for area:** The area $A$ of a rectangle is given by $$A = \text{width} \times \text{length}$$ 3. **Apply the width:** Given width = 4 feet, so $$A = 4x$$ 4. **Set the compound inequality for the area:** The area must satisfy $$12 < 4x \leq 24$$ 5. **Solve the inequality:** Divide all parts by 4: $$\frac{12}{\cancel{4}} < \frac{4x}{\cancel{4}} \leq \frac{24}{4}$$ which simplifies to $$3 < x \leq 6$$ 6. **Interpretation:** The length $x$ must be greater than 3 feet and at most 6 feet to satisfy the area condition. **Final answer:** $$3 < x \leq 6$$