1. Calculate the moles of NaCl in each solution:

* Solution 1: (0.400 L) * (0.420 mol/L) = 0.168 mol NaCl

* Solution 2: (0.110 L) * (0.240 mol/L) = 0.0264 mol NaCl

2. Calculate the total moles of NaCl:

* Total moles = 0.168 mol + 0.0264 mol = 0.1944 mol NaCl

3. Calculate the total volume of the final solution:

* Total volume = 0.400 L + 0.110 L = 0.510 L

4. Calculate the final molarity:

* Final molarity = (Total moles of NaCl) / (Total volume of solution)

* Final molarity = (0.1944 mol) / (0.510 L) = 0.381 M

Therefore, the molarity of the final solution is 0.381 M.