1. **State the problem:** We need to determine the placement of 6 sprinklers to cover a 9 by 16 tile plot, where each sprinkler waters 24 adjacent tiles. 2. **Understand sprinkler coverage:** Each sprinkler covers 24 tiles. Since the plot has 144 tiles, 6 sprinklers cover all tiles. 3. **Calculate sprinkler coverage area:** 24 tiles per sprinkler could be arranged in various shapes, for example, a 4 by 6 tile area (since $4 \times 6 = 24$). 4. **Divide the plot into sections:** The 9 by 16 plot can be divided into 6 sections of 24 tiles each. For example, split the 16 tiles lengthwise into 6 parts of approximately 4 tiles wide (some overlap or adjustment may be needed). 5. **Suggested placement:** Place each sprinkler roughly at the center of each 4 by 6 tile section to maximize coverage. 6. **Summary:** By dividing the plot into 6 equal sections of 24 tiles and placing one sprinkler in the center of each section, all tiles will be watered efficiently. **Final answer:** Place 6 sprinklers evenly spaced so each covers a 4 by 6 tile area, covering the entire 9 by 16 plot.