 Solution

Since $B_{\mathrm{hex}}<B_{\square }$, the hexagonal lattice has larger accessible cell area at any common allowed total area $A>B_{\square }$. HenceThe kinetic entropies cancel at the same temperature. The triangular lattice is favoured and has higher entropy within this cell model, even though both structures look ordered. More efficient packing leaves more local displacement freedom at a fixed number density. This comparison does not by itself establish whether either crystal is stable against the fluid.