Let the length, breadth, and height of the cuboid be \(4x\) meters, \(3x\) meters, and \(2x\) meters respectively. \(\therefore\) According to the question, \(2(4x \cdot 3x + 3x \cdot 2x + 2x \cdot 4x) = 468\) Or, \(2(12x^2 + 6x^2 + 8x^2) = 468\) Or, \(2 \times 26x^2 = 468\) Or, \(x^2 = \frac{468}{2 \times 26}\) Or, \(x = \sqrt{9} = 3\) Now, volume of the cuboid = \(4x \cdot 3x \cdot 2x\) cubic meters \(= 24x^3\) cubic meters \(= 24 \times 3^3\) cubic meters \(= 24 \times 27\) cubic meters \(= 648\) cubic meters \(\therefore\) The volume of the cuboid is 648 cubic meters.