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Introduction:
To solve this problem, we need to find the number of points on the x-axis that are 2 units away from the point (2,4). We can use the distance formula to calculate the distance between two points in a coordinate plane.

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

Given Information:
Point A = (2,4)
Distance from A to any point on the x-axis = 2 units

Method:
To find the number of points on the x-axis that are 2 units away from point A, we can use the distance formula and substitute the y-coordinate of point A with 0 (since the points lie on the x-axis). The x-coordinate of point A remains the same. Let's solve this step by step.

Step 1:
Substitute the values into the distance formula:
distance = sqrt((x2 - 2)^2 + (0 - 4)^2)

Step 2:
Simplify the equation:
distance = sqrt((x2 - 2)^2 + 16)
distance = sqrt(x2^2 - 4x2 + 4 + 16)
distance = sqrt(x2^2 - 4x2 + 20)

Step 3:
Since the distance between the points is 2 units, we can set up an equation:
sqrt(x2^2 - 4x2 + 20) = 2

Step 4:
Square both sides of the equation to eliminate the square root:
x2^2 - 4x2 + 20 = 4

Step 5:
Rearrange the equation:
x2^2 - 4x2 + 16 = 0

Step 6:
Factorize the equation:
(x2 - 2)(x2 - 8) = 0

Step 7:
Set each factor equal to zero and solve for x:
x2 - 2 = 0 or x2 - 8 = 0
x2 = 2 or x2 = 8
x = sqrt(2) or x = sqrt(8)

Step 8:
The points on the x-axis that are 2 units away from point A are:
x = sqrt(2) and x = sqrt(8)

Conclusion:
There are two points on the x-axis that are 2 units away from the point (2,4).