To determine the relationship between the given lines, we need to analyze their equations:

1. The first equation is given as \(x + 2y = 12\).
2. The second equation is \(4x + 8y = 48\).

Let's simplify both equations and compare them:

1. For the first equation \(x + 2y = 12\), it is already in simplified form.
2. Simplifying the second equation \(4x + 8y = 48\) by dividing every term by 4:
   • \(\dfrac{4x}{4} + \dfrac{8y}{4} = \dfrac{48}{4}\)
   • This simplifies to \(x + 2y = 12\).

We see that both equations simplify to the same equation \(x + 2y = 12\). Thus, the two lines are coincident, which means they lie on top of each other and have infinitely many solutions.

Now, let's rule out the other options:

• Are perpendicular to each other: Two lines are perpendicular if the product of their slopes is \(-1\). Here, both lines have the same slope, so this option is incorrect.
• Are parallel: Two lines are parallel if they have the same slope but different intercepts. Since these lines have the same equation, this option is incorrect.
• Pass through the origin: A line passes through the origin if its equation can be expressed in the form \(ax + by = 0\). Here, the lines do not pass through the origin as they intersect the axes at different points not linked to the origin.

Therefore, the correct answer is that the lines are coincident with each other.