If you solve x-2y = 4 for y, then you'll get y = (1/2)x - 2 which is the same as y = 0.5x - 2. The slope is 1/2 which is the same as the slope of the equation y = (1/2)x+6; however the y intercepts are not the same. So we have two parallel lines that never cross. There are no intersection points which means there are no solutions. The system is inconsistent.
Check out the attached image.
