When you have two sides of a triangle given, the third side must be

1. Greater than the difference of the two given sides.
and
2. Less than the sum of the two given sides.

So when you have given sides of 9 and 16, the third side k must be:

1. Greater than the difference 16-9 or 7.

and

2. Less than the sum 16+9 or 25.

So that means that 

       7 < k < 25

On the choices, I. 6, II. 16, and III. 25

only II. 16  lies between 7 and 25

You cannot draw a triangle with sides 9, 16 and 6 because the two sides 9 and 6
can only span lengths less than their sum 16.

You also cannot make a triangle with sides 9,16 and 25 because the sides 9 
and 16 can only span lengths less than, not equal to, ther sum 25.

However you can draw a triangle with sides 9, 16, and 16.  It will, of
course be isosceles.

Edwin