First things first: You'll want to rewrite your equation in y=mx+b form because m is the slope, and the slope of a perpendicular line is the "negative reciprocal."
So, your equation becomes: y = -2x-19 and the slope is -2.
Now you're desired perpendicular line has a slope of 1/2 (note it's the reciprocal and has the opposite sign of the slope of the given line. Being the "negative reciprocal" does not that it's always negative.)
So this gives you as a place to start, the equation:
y = 1/2x + b
You can substitute your point, (-8,-4) into that to solve for b and then rewrite your final answer.
If you need guidance, here it is:
-4 = 1/2(-8) + b (Substitute -4 for y and -8 for x))
-4 = -4 + b (Simplify the 1/2 times -8)
b = 0 (add 4 to both sides to isolate b)
So, your answer is:
y = 1/2x + 0 (continue to use m = 1/2 because it's the slope of the line perpendicular to the given line)
or more properly
y = 1/2x (because we just don't leave " + 0"...