The two equations are linear, meaning that their graphs are straight lines. The solution occurs where the two lines intersect. If the lines are parallel to one another, however, they will never intersect and will thus have no solution. Two lines are parallel if they have the same value for the slope. So let's put these two equations into the slope-intercept form, y = mx + b where m is the slope and b is the y-intercept:
8x - 4y = 1
-4y = -8x + 1
y = 2x - 1/4
So the slope of this line is m = 2. Since we are looking for the value of K for which the two equations have no solution, we are looking for the second line to also have a slope of 2:
2x - Ky = 3
-Ky = -2x + 3
y = (2/K)x - 3/K
For this line to have a slope of m = 2, we must have K=1.
