To answer this problem, you should just substitute some figures in order to get the required amount.
So, let a be the amount of 10% iodide solution
So...
4 (3) + 10a = 6 (3+a)
[4 represents the silver iodine solution, the 3 is the liters, while we are looking for the 6% solution]
12 + 10a = 18 + 6a
10a - 6a = 18 - 12
4a = 6
a = 6/4
a = 3/2
So you will need 3/2 or 1.5 liters of 10% iodide solution.