The required line is perpendicular to -2x + 4y - 1 = 0

-2x + 4y - 1 = 0

=> 4y = 2x + 1

=> y = x/2 + 1/4

This is of the form y = mx + c where the slope is m and the y-intercept is c. Therefore the slope is 1/2.

The required line is perpendicular to -2x + 4y - 1 = 0, so its slope is the negative reciprocal of 1/2 or -2.

The equation of a line through (-2 , 4) and with a slope -2 is

(y - 4) / (x + 2) = -2

=> y - 4 = -2x - 4

=> 2x + y = 0

**The required line is 2x + y = 0**