Two parallel lines have the same slope, so we need to find the slope of the first line y = (1/4)x - 2, and then use it to find the equation of the parallel line that passes through (4, -2).
The slope of the first line is 1/4, so the slope of the parallel line will also be 1/4.
Using the point-slope form of the equation, we can write the equation of the parallel line as:
y - (-2) = (1/4)(x - 4)
Simplifying this equation, we get:
y + 2 = (1/4)x - 1
Subtracting 2 from both sides, we get:
y = (1/4)x - 3
Therefore, the equation of the line that is parallel to y = (1/4)x - 2 and passes through (4, -2) is y = (1/4)x - 3, which is option D.