To find the electric flux density of a material, we need to first understand what electric flux and charge density are.

Electric flux (Φ) is a measure of the electric field passing through a given surface. It is defined as the total number of electric field lines passing through a surface. Mathematically, electric flux is given by Φ = ∮E⋅dA, where E is the electric field vector and dA is the differential area vector.

Charge density (ρ) is a measure of the charge per unit volume. It represents the amount of charge contained within a given volume. Mathematically, charge density is given by ρ = Q/V, where Q is the total charge and V is the volume.

Now, we are given that the charge density is 12 units in a volume region of 0.5 units.

To find the electric flux density, we can use Gauss's Law, which relates the electric flux passing through a closed surface to the total charge enclosed by that surface. Mathematically, Gauss's Law can be expressed as Φ = Q/ε, where ε is the permittivity of the material.

In this case, we are given the charge density (ρ) and the volume (V), so we can calculate the total charge (Q) using the formula Q = ρV.

Given that the charge density (ρ) is 12 units in a volume region of 0.5 units, we can substitute these values into the formula Q = ρV to find the total charge:

Q = 12 units * 0.5 units = 6 units

Now, we can substitute the values of Q and ε into Gauss's Law to find the electric flux density:

Φ = Q/ε

Since the total charge (Q) is 6 units and the permittivity (ε) is not given, we cannot calculate the exact value of the electric flux density. Therefore, none of the provided options (a), (b), (c), or (d) is correct.

In conclusion, the correct answer cannot be determined with the given information.