For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

Where:
m: It's the slope
b: It is the cut point with the y axis.
By definition, if two straight lines are parallel then their slopes are equal. Thus, the slope of the line sought will be 

We substitute the given point to find b:

Finally the line is:

Answer:

Given data:
The first point given iis (a, b)=(-6,2).
The second point given is (c,d)=(0, -6).
The expression for the slope is,
m=(d-b)/(c-a)
Substitute the given points in the above expression.
m=(-6-2)/(0-(-6))
=(-8)/(6)
=-4/3
Thus, the slope of the line is -4/3, so (C) option is correct.
Their both the answer hope this helps