There is a remarkable formula to calculate the distance from a given point to a given straight line in a coordinate plane.


    Let the straight line in a coordinate plane is defined in terms of its linear equation 

         a*x + b*y + c = 0,

    where "a", "b" and "c" are real numbers, and let P = (,) be the point in the coordinate plane. 

    Then the distance from the point P to the straight line is equal to

        d = .


Regarding this formula, see the lesson
    The distance from a point to a straight line in a coordinate plane
in this site.


Your straight line is 2x + 3y - 6 = 0.   The point is  (4,-2)


Substitute the given data  a= 2, b= 3, c= -6,   = 4,  = -2  into the formula to get the distance under the question


     =  =  =  = 1.1094  (approximately).


Answer.  The distance is   = 1.1094  (approximately).