Given, P(0,−4).
Here, the x-coordinate is 0 and y-coordinate is −4.
We know, a point on the x-axis has the form (a,0), where a is any number.
But the given point is in the form (0,a) and therefore lies on the y-axis.
Therefore, the point P(0,4) lies on the y-axis and so, the given statement is false.
Hence, option B is correct.