The given line has an equation of y = 2x + 4 (we can see this from the fact that it passes through the points (1, 6) and (-2, 0)).
To find the equation of the line that is perpendicular to this line and has an x-intercept of 6, we first need to determine the slope of the perpendicular line.
The slope of the given line is 2, so the slope of the perpendicular line is the negative reciprocal of 2, which is -1/2.
Now we can use the slope-intercept form of a line (y = mx + b) and the fact that the x-intercept is (6, 0) to solve for the y-intercept (b):
0 = (-1/2)(6) + b
b = 3
Therefore, the equation of the line that is perpendicular to the given line and has an x-intercept of 6 is y = (-1/2)x + 3, which is option B.