Why is the enthalpy of solution for NaCl 3.88 and not 4.1 kJ/mol?
Your approach is correct. The small discrepancy of the results when using parameter values from different sources could be caused by inconsistent standard states (temperature and pressure), or simply by measurement uncertainty (in this case, the resulting difference would not be considered significant).

By way of comparison, I found the following parameter values for a temperature of $T=25\ \mathrm{^\circ C}=298.15\ \mathrm K$ and a pressure of $p=1\ \mathrm{bar}=100\ \mathrm{kPa}$.


Standard molar enthalpy of formation $\Delta_{\mathrm f}H_{\mathrm m}^\circ(\ce{NaCl(s)})=-411.2\ \mathrm{kJ\ mol^{-1}}$ [1]
Standard molar enthalpy of formation $\Delta_{\mathrm f}H_{\mathrm m}^\circ(\ce{Na+(aq)})=-240.1\ \mathrm{kJ\ mol^{-1}}$ [2]
Standard molar enthalpy of formation $\Delta_{\mathrm f}H_{\mathrm m}^\circ(\ce{Cl-(aq)})=-167.2\ \mathrm{kJ\ mol^{-1}}$ [2]
Standard molar enthalpy of solution $\Delta_{\mathrm{sol}}H_{\mathrm m}^\circ(\ce{NaCl(s)})=3.88\ \mathrm{kJ\ mol^{-1}}$ [3]


Calculating the standard molar enthalpy of solution from the given values for the standard molar enthalpy of formation yields

$$\begin{align}
\Delta_{\mathrm{sol}}H_{\mathrm m}^\circ(\ce{NaCl(s)})&amp;=\Delta_{\mathrm f}H_{\mathrm m}^\circ(\ce{Na+(aq)})+\Delta_{\mathrm f}H_{\mathrm m}^\circ(\ce{Cl-(aq)})-\Delta_{\mathrm f}H_{\mathrm m}^\circ(\ce{NaCl(s)})\\[6pt]
&amp;=-240.1\ \mathrm{kJ\ mol^{-1}}-167.2\ \mathrm{kJ\ mol^{-1}}+411.2\ \mathrm{kJ\ mol^{-1}}\\[6pt]
&amp;=3.9\ \mathrm{kJ\ mol^{-1}}
\end{align}$$

Considering the number of significant digits, there is no significant difference between the calculated result of $\Delta_{\mathrm{sol}}H_{\mathrm m}^\circ(\ce{NaCl})=3.9\ \mathrm{kJ\ mol^{-1}}$ and the corresponding literature value of $\Delta_{\mathrm{sol}}H_{\mathrm m}^\circ(\ce{NaCl})=3.88\ \mathrm{kJ\ mol^{-1}}$.



References

[1] “Standard Thermodynamic Properties of Chemical Substances”, in CRC Handbook of Chemistry and Physics, 90th Edition (CD-ROM Version 2010), David R. Lide, ed., CRC Press/Taylor and Francis, Boca Raton, FL.

[2] “Thermodynamic Properties of Aqueous Ions”, in CRC Handbook of Chemistry and Physics, 90th Edition (CD-ROM Version 2010), David R. Lide, ed., CRC Press/Taylor and Francis, Boca Raton, FL.

[3] “Enthalpy of Solution of Electrolytes”, in CRC Handbook of Chemistry and Physics, 90th Edition (CD-ROM Version 2010), David R. Lide, ed., CRC Press/Taylor and Francis, Boca Raton, FL.