How many valence electrons does the azide ion have?
Nitrogen (the element) has 7 electrons. But two of those electrons are in the $1s$ orbital, and so are not considered valence.  Therefore, a single elemental nitrogen has five valence electrons.

There are three nitrogens, and so $5 \times 3 = 15$ electrons for $\ce{N_3}$.

Finally, azide is $\ce{N_3^{-}}$, there is an additional electron beyond the neutral form.  So, the total number of valence electrons is $15 + 1 = 16$.