An unknown amount of water is mixed with

Question

350 mL of a 6 M solution of NaOH solution.
A 75 mL sample of the resulting solution is
titrated to neutrality with 52.5 mL of 6 M
HCl. Calculate the concentration of the diluted
NaOH solution.
Answer in units of M

I didn't know what to do, so I just converted to moles for the first solution.

Answer 1

HCl + NaOH ==> NaCl + H2O

How many mols HCl used for the titration?
That's mols HCl = M x L = ?
How many mols for NaOH. That must be the same as mols HCl. So you have that many mols NaOH in 75 mL, and (NaOH) = mols/L = ?
All of that business about 350 mL, 6M, unknown amount of water added, etc etc is a red herring. You know the M and volume of the HCl, that gives you mols HCl, that must be the same as mols of the titrated NaOH, and that's what's in the 75 mL of the NaOH. It would have been interesting if the problem asked for the unknown amount of water added. In that case the 350 mL of 6 M would have been needed.