From Na to Si, the melting points increase, with a sharp increase from Na to Mg, and Al to Si, reaching a maximum for Si.
From Si to P, there is a sharp decrease in melting point, followed by a small increase in melting point from P to S, and a decrease in melting point from S to Ar.
Na, Mg, Al all have metallic structure. Moving from Na to Mg to Al, the number of protons and electrons increase, so there is an increasing electrostatic force of attraction between the positive ions and delocalised electrons, pulling the electrons closer to the nucleus, making the metallic bonding stronger. An increasing amount of energy is needed to break the increasing strength of the metallic bonds during melting. This results in the increasing trend of melting points from Na to Al.
Silicon exists as a giant molecular structure. A lot more energy is needed to break the large number of covalent bonds in the giant molecular structure, resulting in Silicon’s very high melting point.
Phosphorus, sulfur, chlorine and argon are non-metals which have simple covalent structures, with weak intermolecular forces of attraction. These forces require less energy to break during melting, resulting in their relatively lower melting points.
Phosphorus exists as P4 molecules, sulfur exists as S8 molecules, chlorine exists as Cl2 molecules and argon exists as individual atoms. The strength of the intermolecular forces of attraction decreases as the size of the molecule decreases, so melting points decrease from S to P to Cl to Ar. This explains the slight increase in melting point from phosphorus to sulfur, as sulfur molecules are bigger in mass than phosphorus molecules.