Assuming that the percentage alcohol in the original solution is % by volume, 12ml of 12% alcohol solution contains 12 * 12 /100 = 1.44ml of pure alchohol.
If we let X = the final volume of the 6% v/v alcohol solution we wish to make then we can write the following equation
6 = 1.44/x * 100
Multiplying both sides of the equation by x we get;-
6x=100*1.44
x=144/6
x=24
Therefore if the final volume of the 6% solution is 24ml, we need to add;-
(24-12) = 12 ml of water.
