When we have two perpendicular lines their slopes are opposite and inverse.
In this case, we have the equation of the line:
y-6x= -3
Let's solve for y and arrange this equation to make it look like the general form of a linear equation: y=mx+b, where m is the slope of the line.
y-6x= -3
y-6x+6x= -3+6x
y= 6x-3
As we can see, the number that is multiplying the x variable in our equation is 6, the slope of this line is 6.
As mentioned, a perpendicular line to the line y= 6x-3 would have a slope opposite and inverse, then the slope of the line perpendicular to the first line (m2) would be:
from the options that we have, we can see that the only line that has a slope of -1/6 is the line y= -1/6+8, so that is the right option.