I think you are on the right track. But first, we have to get the signs of those two experimental reactions right. This is a case where the online approach is not good. When you do these reactions and measure the temperature changes in the lab, it's much easier to see and understand what's happening.
Here are the four "given" reactions, with their corresponding ΔHs:
NH3 (g) ––�?gt; NH3 (aq) ΔH = �?4640 J/mol
HCl (g) ––�?gt; HCl (aq) ΔH = �?5140 J/mol
NH4Cl (s) ––�?gt; NH4Cl (aq) ΔH = +15428.82 J/mol
NH3 (aq) + HCl (aq) ––�?gt; NH4Cl (aq) ΔH = �?4718.6 J/mol
The "desired" reaction is
NH4Cl (s) ––�?gt; NH3 (g) + HCl (g) ΔH = ?
So, you need to add the four given reactions in such a way so that you get this reaction.
Hint: Notice, for example, that the desired reaction has 1 NH4Cl (s) on the left side. The third given reaction also has 1 NH4Cl (s) on the left side. None of the other given reactions have NH4Cl (s) in them. Therefore, the third reaction is OK as is, you do not have to reverse it or anything. Also, you will need to use each given reaction only once.
Steve