Molarity is moles of solute per liter of solution, so in order to find the molarity of the carbonate ion in the final solution, we need to find the total number of moles of carbonate ion and divide it by the total volume of the solution in liters.
There is one mole of carbonate ion (CO3) per mole of sodium carbonate (Na2CO3), so using the appropriate stoichiometry, we find that the first solution contains [(0.373 moles of sodium carbonate)/(liter)]*[(1 mole of carbonate ion)/(mole of sodium carbonate)]*[(1 liter)/(1000 mL)]*[42.1 mL] = 0.0157 moles of carbonate ion.
Similarly, there is one mole of carbonate ion (CO3) per mole of potassium carbonate (K2CO3), so the second solution contains [(0.311 moles of potassium carbonate)/(liter)]*[(1 mole of carbonate ion)/(mole of potassium carbonate)]*[(1 liter)/(1000 mL)]*[24.0 mL] = 0.00746 moles of carbonate ion.
Thus, the final solution contains 0.0157 + 0.00746 = 0.0232 moles of carbonate ion.
To find the volume of the final solution we simply add the volumes of the two solutions, so we get 42.1 mL + 24.0 mL = 66.1 mL. Converting this to liters gives us (66.1 mL)*[(1 L)/(1000 mL)] = 0.0661 L.
The concentration of carbonate ion in the final solution is therefore (0.0232 moles)/(0.0661 L) = 0.350 moles/L = 0.350 M.