Explain theoretically the Lewis structure diagram of covalent compound \[\mathbf{A}{{\mathbf{l}}_{2}}\mathbf{C}{{\mathbf{l}}_{6}}\]?

Hint: A Lewis structure is a very simple way to represent the valence shell electrons of a molecule. It gives an idea on how the electrons are paired/arranged around an atom in the molecule. In Lewis dot structure, each electron can be represented in the form of dots and for bonding the electrons a line is drawn that connects the dots.

Complete answer:
-Here, in \[AlC{{l}_{3}}\] , it has $6$ bonds which are covalent and $2$ bonds which are coordinated. Also, Chlorine contains $17$ electrons from which $10$ electrons are occupied in the\[1S\],$2S$ and $2P$ orbitals. The remaining $7$ are distributed in the $3S$ and the three $3P$orbitals but after the formation of covalent bonds, these orbitals hybridise into the SP orbitals.
-Chlorine thus has $7$ electrons which are in the \[4\text{ }S{{P}^{3}}\] orbitals where $3$ orbitals are filled with $2$ electrons each and the ${{4}^{th}}$ has only $1$ left with it. Here, aluminium has just $3$ electrons with it, on which $2$ are in the $3S$ and $1$ is in one of the $3P$ orbitals. However, after the hybridization of these $3$ electrons, they get spread over the \[4\text{ }S{{P}^{3}}\] orbitals.
-Actually, chlorine has a very high electronegativity because of which it pulls really hard at electrons from other atoms. So now, the Chlorine atoms have been satisfied in their hunger for electrons as they have a full set of 8 electrons. Because of this "diminished appetite" happening on the side of the Chlorine atoms and also due to the increased hunger on the part of the Aluminium atom, finally the bond is created by both of the Chlorine electrons.

Note:
The Lewis structure is the most limited and simplest theory, it does not explain how the bonds are formed or how the electrons are shared in between the atoms. And this is considered to be the basic limitation of Lewis structure.