I assume you need to find the shortest possible distance between the Q and R? And I don't have any idea what methods you used to find the distance between the 2 circles, but these two don't intersect.

The equation for the first circle should be converted to a useful form by completing the square:

So this circle is centered at (3,-1) and has a radius of 5.

Draw a line segment from the center of one circle to the center of another. The length of this segment is:

The shortest distance between the circles is this distance minus the two radii, which is 4 units. So the minimum distance between P and Q is 4.