First, make the equation 2y+4x=12 into a linear equation(y=mx+b)
From this, you know the slope is -2.
The perpendicular of any slope is going to be the negative inverse.
negative inverse: a/b-->-b/a
so basically flip it and make it negative(make it positive if the original is negative).
So, for -2 it would be 1/2
Now right the equation for the perpendicular line.
b is the y intercept, and since you want to make the line go through (8,1) you have to change the 6 in the original equation.
To do this replace x and y with 8 and 1
So you plug that into the equation