Step 1 :Define the variables: the mass of the mothership \(M = 180\) xons, the mass of the cruiser \(m = 12.0\) xons, and the distance between the mothership and the cruiser \(d = 225\) xiles.
Step 2 :Calculate the position of the center of mass using the formula \(x_{cm} = \frac{M*0 + m*d}{M + m}\).
Step 3 :Substitute the given values into the formula to get \(x_{cm} = \frac{180*0 + 12.0*225}{180 + 12.0} = 14.0625\).
Step 4 :The final position of the two spacecraft when they are pulled together by the tractor beam is \(\boxed{14.0625}\) xiles.