Final answer:
The equations are coincident, representing the same line.
Step-by-step explanation:
To determine if the equations are intersecting, parallel, or coincident, we can compare the slopes and y-intercepts of the two equations.
Equation 1: x + 2y = 6
Equation 2: 4x + 8y = 24
We can rewrite both equations in slope-intercept form, y = mx + b.
Equation 1: y = -1/2x + 3
Equation 2: y = -1/2x + 3
Since both equations have the same slope (-1/2) and same y-intercept (3), they are coincident and represent the same line.