To find the point on the y-axis that is equidistant from the given points (2, 3) and (-4, 1), we can use the concept of distance formula and the properties of perpendicular bisectors.

Distance Formula:
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]

Perpendicular Bisector:
A perpendicular bisector is a line that intersects another line segment at a right angle and divides it into two equal parts.

Now, let's solve the problem step by step:

1. Plot the given points:
Plot the points (2, 3) and (-4, 1) on a coordinate plane.

2. Find the midpoint of the line segment:
Using the midpoint formula, find the coordinates of the midpoint of the line segment connecting the given points.
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
Midpoint = [(2 + (-4))/2, (3 + 1)/2]
Midpoint = [-2/2, 4/2]
Midpoint = (-1, 2)

3. Find the slope of the line segment:
Using the slope formula, find the slope of the line segment connecting the given points.
Slope = (y2 - y1)/(x2 - x1)
Slope = (1 - 3)/(-4 - 2)
Slope = -2/-6
Slope = 1/3

4. Find the slope of the perpendicular bisector:
Since the perpendicular bisector is perpendicular to the line segment, the slope of the perpendicular bisector will be the negative reciprocal of the slope of the line segment.
Slope of the perpendicular bisector = -1/(1/3)
Slope of the perpendicular bisector = -3

5. Find the equation of the perpendicular bisector:
Using the point-slope form of a line, we can find the equation of the perpendicular bisector using the slope (-3) and the midpoint (-1, 2).
y - y1 = m(x - x1)
y - 2 = -3(x - (-1))
y - 2 = -3(x + 1)
y - 2 = -3x - 3
y = -3x - 1

6. Find the point of intersection with the y-axis:
To find the point on the y-axis, we substitute x = 0 into the equation of the perpendicular bisector.
y = -3(0) - 1
y = -1

Therefore, the point on the y-axis that is equidistant from the points (2, 3) and (-4, 1) is (0, -1).

Hence, the correct answer is option 'A' (0, -1).