1. We need to count how many of the given molecules contain a covalent bond between two atoms of the same element.

   The list is: $B_2H_6,\, B_3N_3H_6,\, N_2O,\, N_2O_4,\, H_2S_2O_3,\, H_2S_2O_8$

2. Check each molecule one by one.

(i) $B_2H_6$

Structure of diborane contains a direct $B-B$ linkage along with bridge hydrogens. So it has a covalent bond between same kind of atoms.

✅ Count this molecule.

(ii) $B_3N_3H_6$

This is borazine. Its ring structure is alternating: $-B-N-B-N-B-N-$ There is no $B-B$ or $N-N$ bond in the ring. So it does not contain a bond between same kind of atoms.

❌ Do not count.

(iii) $N_2O$

Nitrous oxide has the skeleton: $N-N-O$ So there is an $N-N$ covalent bond.

✅ Count this molecule.

(iv) $N_2O_4$

Dinitrogen tetroxide has structure with an $N-N$ bond: $O_2N-NO_2$ So it contains a covalent bond between same atoms.

✅ Count this molecule.

(v) $H_2S_2O_3$

Thiosulfuric acid has structure analogous to sulfuric acid, with one oxygen replaced by sulfur. Hence it contains an $S-S$ bond. So it has a covalent bond between same kind of atoms.

✅ Count this molecule.

(vi) $H_2S_2O_8$

Peroxodisulfuric acid has structure: $HO_3S-O-O-SO_3H$ It contains an $O-O$ peroxo bond between same kind of atoms.

✅ Count this molecule.

3. Total counted molecules: $B_2H_6,\, N_2O,\, N_2O_4,\, H_2S_2O_3,\, H_2S_2O_8$

So total number is $5$

4. Comparison with stored correct answer:

• Stored correct answer: $4$
• Derived answer: $5$

The stored answer seems incorrect because $H_2S_2O_8$ definitely contains an $O-O$ covalent bond, and $H_2S_2O_3$ contains an $S-S$ covalent bond; along with $B_2H_6$, $N_2O$, and $N_2O_4$, the total becomes 5.