The distance between the point (0,4) and the line 4x - 6y + 12 = 0 is calculated. Using the formula for distance from a point to a line, the distance is found to be (18*sqrt13)/13.

1. Calculate the distance between the points (0,4) and the line 4x - 6y +12 = 0.
Solution
The distance d between the point (x1,y1) from the line ax+by+c = 0 is given by the formula:
d = | (ax1+by1+c)/sqrt(a^2+b^2)
The given point (x1,y1) = (0,4).
The line is 4x-6y+12 = 0.
So the distance d = |(4*0-6*4-12)/sqrt{(4^2+(-6)^2}
d = |-36/sqrt(16+36)|
d = 36/sqrt52
d = 18/sqrt13
d = (18*sqrt13)/13 is the distance of the point (0, 4)and the line 4x-6y+12 = 0.