1. State the problem: We need to find the value of $x$ such that the volume of a rectangular solid with dimensions 2, 8, and $x$ equals the volume of a cube with side length 4. 2. Write the volume formulas: - Volume of the rectangular solid = $2 \times 8 \times x = 16x$ - Volume of the cube = $4^3 = 64$ 3. Set the volumes equal and solve for $x$: $$16x = 64$$ Divide both sides by 16: $$x = \frac{64}{16} = 4$$ 4. Final answer: The value of $x$ is $4$.