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Carbon and silicon belong to the group $4$.The maximum coordination of carbon in a commonly occurring compound is $4$, whereas that of silicon is $6$.This is due to:
$A.$ Large size of silicon
$B.$ More electro-positive nature of silicon
$C.$ Availability of $d - $ orbital in silicon
$D.$ Both $A\& B$

Answer
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Hint:Coordination number of an atom in an organic molecule is the number of atoms directly bonded to it and the maximum coordination number is the number of maximum atoms directly bonded to central species.

Complete step by step answer:
We know carbon and silicon belong to the same group; the atomic number of carbon is $6$ whereas the atomic number of silicon is $14$.The maximum coordination of carbon is four whereas for silicon it is six because in carbon there is no $d - $ orbital to expand but in case of silicon it has vacant $d - $ orbital in its valence shell so it can expand its valency using these available vacant $d - $ orbital and form 6 coordinated compounds. So the maximum coordination number of silicon is $6$ .

So, the correct option is $C.$

Additional information: The main difference of carbon and silicon. Given table summarizes the difference between carbon and silicon.
CarbonSilicon
It has two electron in the penultimate shellIt has eight electron in the penultimate shell
No vacant $d - $ orbital presentPresent vacant $d - $ orbital
It does not form complex compoundIt forms a number of complex compounds because of availability of $d - $ orbital in the valence shell.
Carbon has a tendency to form long chain of identical atomsSilicon has a lesser tendency to form a long chain of identical atom
It is a black solidIt is a reddish brown solid


Note:
Most common oxidation state of silicon is $ + 4$ and its valency four. There are few silicon compounds in which coordination number is 5 that are Silatranes. There is only one silicon compound in which coordination number is 6 that is hexafluorosilicate anion. That is a special case and reliant on the high electronegativity of fluorine, the strength of silicon-fluoride bonds that make fit six fluorine atoms around a silicon atoms but the hexafluoro carbonates can’t exist because carbons atoms has no vacant $d - $ orbital.