The volume of the solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis can be found using the disk method. The disk method involves slicing the solid into thin disks perpendicular to the axis of rotation and summing up the volumes of all the disks.

In this case, the radius of each disk is given by the function y = 2x, and the thickness of each disk is given by dx. The volume of each disk is given by the formula:

Volume of disk = π * (radius)\(^2\) * thickness

Substituting the values of the radius and thickness, we get:

Volume of disk = π * (2x)\(^2\) * dx

The total volume of the solid is given by the definite integral of this expression from x = 0 to x = 3:

Volume of solid = \(\int^{3}_{0}\) π * (2x)\(^2\) * dx

Evaluating this definite integral, we get:

Volume of solid = π * \(\int^{3}_{0}\) (4x\(^2\)) * dx

Volume of solid = 4π * \(\int^{3}_{0}\) x\(^2\) * dx

Volume of solid = 4π * [x\(^3\)/3]\(^{3}_{0}\)

Volume of solid = 4π * [(3\(^3\))/3 - (0\(^3\))/3]

Volume of solid = 4π * [27/3]

Volume of solid = 36π cubic units

So, the volume of the solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis is 36π cubic units.