Question 1182678
Here's how to calculate the moment of inertia of the solid:

1. **Describe the shape:** The region bounded by y = 3, x = 2, y = -3, and x = 0 is a rectangle. When revolved about the y-axis, this rectangle forms a hollow cylinder (or a cylindrical shell).

2. **Dimensions of the cylinder:**
    * Inner radius (r₁): 0
    * Outer radius (r₂): 2
    * Height (h): 3 - (-3  We are not given a density, so we'll assume a uniform density (ρ). Then, we will find the moment of inertia *in terms of ρ*. If you're given a density, you would multiply by it at the end to get a numerical moment of inertia.

4. **Moment of Inertia of a hollow cylinder:** The moment of inertia (I) of a hollow cylinder about its central axis is given by the formula:

   I = (1/2) * m * (r₁² + r₂²)

   where m is the mass of the cylinder.

5. **Mass in terms of density and volume:** The mass of the cylinder is equal to the product of its density and volume.  
    * The volume of the hollow cylinder is given by V = πh(r₂² - r₁²)
    * Volume: V = π * 6 * (2² - 0²) = 24π
    * Thus, the mass m = ρ * V = 24πρ

6. **Substitute and calculate:**

   I = (1/2) * (24πρ) * (0² + 2²)
   I = 12πρ * 4
   I = 48πρ

Therefore, the moment of inertia of the solid is $\boxed{48\pi\rho}$.  If the density (ρ) were given, you would multiply by that value to find the numerical moment of inertia.