A stock aqueous solution contains 348.29 grams of NaCl per 1.000L. 68.00mLs of water is added to 10.00mLs of the stock solution. What is the molarity of the dilution???

What is the molarity of the original solution? That will be 348.29 g/molar mass NaCl = moles and that is in 1.000L so that is the molarity.

Technically you can't determine the molarity of the diluted solution because you don't give the density. IF you make the assumption that the 10.00 mL stock solution adds exactly to the 68.00 mL of water to make 78.00 mL of diluted solution, then the new molarity is Old M x (10.00/78.00) = ??