1. Octet rule exceptions are mainly of three types:
   • Incomplete octet: central atom has fewer than 8 electrons
   • Odd-electron molecules: total valence electrons are odd
   • Expanded octet: central atom has more than 8 electrons

We check each molecule one by one.

2. Analyze each species

   1. $\mathrm{CO}_2$ Structure: $\mathrm{O=C=O}$ Carbon has 8 electrons around it.

      Obeys octet

   2. $\mathrm{NO}_2$ Total valence electrons: $5 + 2\times 6 = 17$ Odd number of electrons, so it is an odd-electron molecule.

      Exception to octet

   3. $\mathrm{H}_2\mathrm{SO}_4$ Sulfur in the usual Lewis structure has expanded octet.

      Exception to octet

   4. $\mathrm{BF}_3$ Boron forms 3 bonds and has only 6 electrons around it.

      Incomplete octet → Exception

   5. $\mathrm{CH}_4$ Carbon has 4 bonds  8 electrons.

      Obeys octet

   6. $\mathrm{SiF}_4$ Silicon forms 4 bonds  8 electrons around Si.

      Obeys octet

   7. $\mathrm{ClO}_2$ Total valence electrons: $7 + 2\times 6 = 19$ Odd-electron molecule.

      Exception to octet

   8. $\mathrm{PCl}_5$ Phosphorus has 5 bonds  10 electrons around P.

      Expanded octet → Exception

   9. $\mathrm{BeF}_2$ Beryllium forms 2 bonds and has only 4 electrons around it.

      Incomplete octet → Exception

   10. $\mathrm{C}_2\mathrm{H}_6$ Each carbon has 4 bonds  octet satisfied.

       Obeys octet

   11. $\mathrm{CHCl}_3$ Carbon forms 4 bonds  octet satisfied.

       Obeys octet

   12. $\mathrm{CBr}_4$ Carbon forms 4 bonds  octet satisfied.

       Obeys octet

3. Count the exceptions

   Exceptions are: $\mathrm{NO}_2,\ \mathrm{H}_2\mathrm{SO}_4,\ \mathrm{BF}_3,\ \mathrm{ClO}_2,\ \mathrm{PCl}_5,\ \mathrm{BeF}_2$

   Total number: $6$

4. Comparison with stored answer

   Stored correct answer = $6$

   Our derived answer = $6$

   Hence, they agree.