The equation y = 6x + 2 is in the format which is called the slope-intercept form: y = mx + b where m = slope. Therefore the slope here is 6.
For the line perpendicular, the slope of it is a negative reciprocal from the original slope, that is m(perpendicular) = -1/m
Slope the line perpendicular is m(perpendicular) = -1/6. The answer is C.