Given that one of the roots of the equation $2x^3 - 9x^2 + 12x - 4 = 0$ is $x = 2$, we need to find the other two roots.
One way to solve this equation is to use polynomial long division or synthetic division to divide $2x - 4$ (which is $x - 2$ with a common factor of $2$) into the polynomial $2x^3 - 9x^2 + 12x - 4$. This will give us a quadratic equation that we can solve using the quadratic formula or factoring.
Using synthetic division, we get:

2 | 2 -9 12 -4
| 4 -10 4
-------------
2 -5 2 0

Therefore, the quadratic equation we get is $2x^2 - 5x + 2 = 0$. We can solve this equation using factoring or the quadratic formula:
Factoring:
$$2x^2 - 5x + 2 = 0$$

$$(2x - 1)(x - 2) = 0$$

$x = \frac{1}{2}$ or $x = 2$

Therefore, the three roots of the equation $2x^3 - 9x^2 + 12x - 4 = 0$ are $x = 2$, $x = \frac{1}{2}$, and $x = 2$.