The equation of a plane containing the line of intersection of the planes $$2x - y - 4 = 0$$ and $$y + 2z - 4 = 0$$ and passing through the point (1, 1, 0) is:

We want a plane which simultaneously satisfies two conditions: it must contain every point lying on the common line of the two given planes $$2x - y - 4 = 0$$ and $$y + 2z - 4 = 0$$, and it must also pass through the specific point (1, 1, 0). Because all planes through the line of intersection of two planes can be written as a linear combination of their equations, we first write the general family of such planes.

The standard result (or “formula”) is: if two planes are $$P_1 = 0$$ and $$P_2 = 0,$$ then every plane that contains their intersection line can be expressed as $$P_1 + \lambda P_2 = 0,$$ where $$\lambda$$ is a real parameter.

Here, $$P_1$$ and $$P_2$$ are

$$P_1:\;2x - y - 4 = 0,$$

$$P_2:\;y + 2z - 4 = 0.$$

So we write the required family:

$$\bigl(2x - y - 4\bigr) + \lambda\bigl(y + 2z - 4\bigr) = 0.$$

Now we expand and collect like terms:

$$2x - y - 4 + \lambda y + 2\lambda z - 4\lambda = 0.$$

Grouping the coefficients of $$x,\,y,\,z$$ and the constant term, we have

$$2x + (-1 + \lambda)\,y + 2\lambda\,z + (-4 - 4\lambda) = 0.$$

Next, this plane must pass through the point (1, 1, 0). We substitute $$x = 1,\;y = 1,\;z = 0$$:

$$2(1) + (-1 + \lambda)(1) + 2\lambda(0) + (-4 - 4\lambda) = 0.$$

Simplifying step by step:

$$2 + (-1 + \lambda) + 0 + (-4 - 4\lambda) = 0,$$

$$\bigl(2 - 1 - 4\bigr) + \bigl(\lambda - 4\lambda\bigr) = 0,$$

$$(-3) + (-3\lambda) = 0,$$

$$-3(1 + \lambda) = 0.$$

This gives $$1 + \lambda = 0,$$ so

$$\lambda = -1.$$

We substitute $$\lambda = -1$$ back into the general family equation:

$$2x - y - 4 + (-1)\bigl(y + 2z - 4\bigr) = 0.$$

Distributing the minus sign:

$$2x - y - 4 - y - 2z + 4 = 0.$$

Combining like terms:

$$2x - 2y - 2z + ( -4 + 4 ) = 0,$$

$$2x - 2y - 2z = 0.$$

All coefficients have a common factor 2, which we divide out to simplify:

$$x - y - z = 0.$$

This simplified equation exactly matches Option C.

Hence, the correct answer is Option C.