Let's focus on how much silver iodide we have and how much we obtain.
6 liters of a 4% solution constitutes 6(0.04) liters of silver iodide:
0.24 liter. Let x be the number of liters of the 10% solution. The amount of silver iodide in that is 0.10(x).
Adding together these two volumes of silver iodide:
0.24 liter + 0.10x = 0.06(6 + x) liters
Then 0.24 + 0.10x = 0.36 + 0.06x
Simplifying, 0.04x = 0.12. Dividing both sides by 0.04, x = 0.12/0.04 = 3
3 liters of the 10% solution are needed in order to end up with a 6% solution of silver iodide.
Check: 0.04(6) + 0.10(3) = ? 0.06(6+3)
0.54 = ? = 0.06(9)
0.54 = ? = 0.54 Yes. So, our result is correct.
