Suppose r varies directly as the square of​ m, and inversely as s. if r equals 15r=15 when m equals 8m=8 and s equals 4s=4​, find r when m equals 16m=16 and s equals 4s=4.

Symbolically,

      k*m^2
r=  ---------
           s

Now replace r with 15 and m with 8.  Calculate the constant of proportionality k:
          k(8)^2
15 = ----------     Solve this for k by dividing both sides of this equation by    
              4

    4                            4
------- .    We get    ------- * 15 = k, and this simplifies to 60/64 = 15/16.
 8^2                         8^2

Then your function r   is   

      k*m^2      15 *m^2
r=  --------- = -------------
           s           16s

You are to find r when m equals 16 and s equals 4.  This would be:

      k*m^2      15 *m^2               15*16^2       15(16)
r=  --------- = -------------  => r = -------------- = ------------ = 60 (answer)
           s           16s                      16*4                4