How do I go about solving this problem?
As a follow-up to Steven G.'s answer, one of the most common forms for the equation of a line is the slope-intercept form, y=mx+b, where the 'm' is the slope in the form of a fraction (rise over run, or change in y over change in x) and b is the point on the y-axis where the line crosses, or the y-intercept.
In this question, as Steven has pointed out, two parallel lines, by definition, have the same slope. The x-axis has a slope of zero. This can be determined by taking two points on the x-axis, (0,0) and (1,0) and dividing the change in y, 0-0=0, by the change in x, 1-0=1. So the slope is 0/1=0. Therefore, m=0 and mx=0*x=0. So now, y=b
We've determined that the line is 6 units below the x-axis. The x-axis crosses the y-axis where y=0. 6 units below this point is the y-intercept of the line, at y=-6. Therefore, the equation of your line y=b is y=-6.