Answer:
24 ounces
Step-by-step explanation:
Here's a more intuitive approach to use here.
You know that your initial solution has a percent concentration, presumably volume by volume, of  
25
%
. This means that any volume of this solution contains  
1
 part solute and  
3
 parts solvent.
The target solution must have a concentration of  
10
%
, which means that any volume of this solution will contain  
1
 part of solute and  
9
 parts solvent.
Your starting solution has a volume of  
16
 ounces, or  
4
 parts, each with a volume of  
4
 ounces.
In order to get to a solution that has a total of  
10
 parts, you must add  
6
 parts of solvent to the initial solution. Since we know that
1 part  
=
 4 ounces
it follows that you must add
6
parts
⋅
4 ounces
1
part solvent
=
24 ounces
of distilled water, which is your solvent, to the initial solution.
The target solution will contain  
1
 part solute and  
9
 parts distilled water for a total of  
10
 parts of solution, and hence have a percent concentration of  
10
%
.