The equation $x = 4$ represents a vertical line that passes through the point $(4, y)$ for any value of $y$. Any line parallel to this will also be a vertical line, meaning its equation will be of the form $x = c$, where $c$ is a constant.

Since the line must pass through the point $(3, 2)$, the equation of the line will be:

$x = 3$

Thus, the equation of the line parallel to $x = 4$ and passing through $(3, 2)$ is $x = 3$.

Would you like more details or have any questions?

Here are five related questions:

1. What is the equation of a line parallel to $y = 5$?
2. How do you determine the equation of a line perpendicular to $x = 4$?
3. How can you find the distance between two vertical lines, such as $x = 4$ and $x = 3$?
4. What is the general form of the equation for vertical lines?
5. Can a vertical line have a slope? If not, why?

Tip: Vertical lines always have an undefined slope because they do not change in the $y$-direction.