Explanation:

Lets say DE is line that cuts two concentric circle,so DE=16 cm and it is chord of big circle and HG is chord of small circle and equals 4,also DA=AE=R and HA=AG=r,because point A is center of two circles, lets make AF to be perpendicular of DE line,as we see in picture
Triangle DAE is Isosceles,because of that AF is also median,so DF = DE/2=8,now because DAF is right angle triangle we can use Pythagoras theorem.
AF^2+DF^2=R^2,AF^2+64=R^2,AF^2=R^2–64.
same goes for HAG triangle,AF is median also because HAG triangle is isosceles and HF=HG/2=2,use Pythagoras theorem in HFA right angle triangle.
AF^2+HF^2=r^2,AF^2+4=r^2,AF^2=r^2–4.
R^2–64=r^2–4,R^2-r^2=60