M1=0.25M V1=25mL M2=0.12M
Here's how you can think about what's going on.
You have a
#C = n/V#
When you perform a dilution, you essentially keep the number of moles of solute constant, and increase the total volume of the solution.
In your case, this tells you that both solutions will have the same number of moles of sulfuric acid.
So, how many moles of sulfuric acid you get in your initial solution?
#n = C * V = "0.25 M" * 25 * 10^(-3)"L" = "0.00625 moles"#
What volume of the second solution would contain the same number of moles of sulfuric acid?
#V = n/C = (0.00625color(red)(cancel(color(black)("moles"))))/(0.12color(red)(cancel(color(black)("moles")))/"L") = "0.05208 L" = "52.08 mL"#
So, how much water must do you need to add to the first solution to get its volume to
#V_"add" = "52.08 mL" - "25 mL" = "27.08 mL"#
Rounded to two sig figs, the answer will be
#V_"add" = color(green)("27 mL")#