To determine the y-intercept of line B, you need to find the equation of line B based on the given information.
Since lines A and B are perpendicular, their slopes are negative reciprocals of each other. The equation of line A is x + 2y - 4 = 0, which can be rewritten as 2y = -x + 4 or y = -1/2 * x + 2.
To find the slope of line A, notice that the coefficient of x is -1/2. The slope of line B would be the negative reciprocal of the slope of line A, which is 2.
Now that we know the slope of line B is 2 and that it has the same x-intercept as line A, we can use the point-slope form of a linear equation to find the equation of line B.
Using the x-intercept, we have a point with coordinates (4, 0) since the x-intercept is the value of x when y = 0. Plugging in this point and the slope into the point-slope form (y - y1 = m(x - x1)), the equation of line B becomes:
y - 0 = 2(x - 4)
y = 2x - 8
So, the equation of line B is y = 2x - 8. By comparing it to the general form of a linear equation (y = mx + b), we can see that the y-intercept of line B is -8.
Therefore, the correct answer is option A: -8.