Avogadro number is equal to: 

Avogadro number represents the number of atoms present in 1 mole of an atom. It is also known as the number of molecules present in 1 mole of a substance.

A material's mole is its mass when it has exactly the same number of basic units as that substance, such as 12.0 g of C. The number of atoms in 12.0 g of carbon, or the number of atoms in 1 mole of atom, is known as Avogadro's number. Similar to this, Avogadro's number indicates the quantity of molecules in 1 mole of a material.
Eg. NH₃ has a molecular weight of 17 g/mol.
Therefore, Avogadro's number of NH₃ molecules are present in 1 mole of NH₃, or 17g of NH₃.
Using the charge of 1 mole of electrons and the charge of 1 electron, Avogadro's number is calculated.
1 mole of electrons has a charge of 96485.3383 Coulombs.

Charge of 1 electron $=1.60217653\times {10}^{-19}$ Coulombs
Avogadro's number $=\frac{\text{ Charge of }1\text{ mol electron }}{\text{ Charge of }1\text{ electron }}$
Avogadro's number $=\frac{96485.3383}{1.60217653\times {10}^{-19}}$
Avogadro's number $=6.023\times {10}^{-19}$

Avogadro's number $=6.023\times {10}^{23}$

Hence option C is correct.