Geometry

Let's create a system of equations to solve this question. 

First, we know that the two points must be on the equation $x^2+y^2=25$

We also know that x must be 4. 

Thus, plugging in x=4 into the first equation, we can find y values. We have

$4^2+y^2=25\\ y^2=25-16\\ y=\pm\sqrt9\\ y=3, y=-3$

Thus, the two points A and B are $(4, 3), (4, -3)$

Since they share an x value, the difference between the y values is the distance. We have

$3-(-3)=6$

Thus, 6 is our final answer. 

Thanks! :)