The terms of an infinitely decreasing G.P. having common ratio r  in which all the terms are positive, the first term is 4, and the difference between the third and fifth terms is 32/81, then 

Given that  $a=4,T_3-T_5=32/81$ . Hence, 
 $a(r^2-r^4)=32/81$
Or  $r^4-r^2+8/81=0$ 
Or  $81r^4-81r^2+8=0$
Or  $(9r^2-8)(9r^2-1)=0$
 $\therefore r^2=8/9.1/9$
Therefore, the value of  r  is to be positive since all the terms are positive. 
For $r=1/3$  , $\frac{2\sqrt{2}}{3}$  $S_{\infty }=\frac{a}{1-r}=\frac{4}{1-\frac{1}{3}}=\frac{4\times 3}{2}=6$