The equations for two lines in the coordinate plane are 2dx - y = -4 and 4x - y = -6, where d represents an unknown value. what value(s) of d would make these lines perpendicular?

First, let's put both lines in Slope-intercept form (y = mx + b) to make it a bit easier:
Line A:
2dx - y = -4
-y = -4 - 2dx
y = 2dx + 4

Line B:
4x - y = -6
-y = -6 - 4x
y = 4x + 6

We want a value for d so that line A is perpendicular to line B, which has a slope of 4. That means that the slope of line A must equal -1/4. 
2d = -1/4
d = -1/8