The correct order of increasing metallic character of Na, Be, P, Mg...

Metallic character is the tendency of an element to lose electrons. It decreases across a period from left to right and increases down a group.

The elements $\text{Na}$, $\text{Mg}$, $\text{Si}$, and $\text{P}$ belong to the third period. Across a period, metallic character decreases, so the order is $\text{Na} > \text{Mg} > \text{Si} > \text{P}$.

The elements $\text{Be}$ and $\text{Mg}$ belong to Group 2. Down a group, metallic character increases, so $\text{Mg} > \text{Be}$.

Comparing $\text{Be}$ (a metal) with $\text{Si}$ (a metalloid)$and \text{P}$ (a non-metal), $\text{Be}$ is more metallic than both $\text{Si}$ and $\text{P}$.

Combining these observations, the increasing order of metallic character is $\text{P} < \text{Si} < \text{Be} < \text{Mg} < \text{Na}$.

Answer: $P < Si < Be < Mg < Na$