(2,4) is 4 units away from the x-axis. There are no points on the x-axis that are 2 units away from (2,4).
The closest is (2,0)
You can have a circle with radius 2 and centered at (2,4).
That will give you ALL of the points that are exactly 2 units away from (2,4)
The equation of this circle is (x-2)^2 + (y-4)^2 = 4
Now you can generate an unlimited number of points that are
exactly 2 units away from (2,4) by selecting a value for x or y
and then solving.
For example, if x=0 then y=4, so (0,4) is exactly 2 units away from (2,4)
if y=0, then (x-2)^2 + 16 = 4
(x-2)^2 = -12
So the circle does not intersect the x axis, as described in the opening statement
in bold above