Check option A: Boric acid is a protonic acid

Boric acid is $\mathrm{H_3BO_3}$ or $\mathrm{B(OH)_3}$. It does not act as a proton donor in the usual Brønsted sense.

Instead, it behaves as a Lewis acid by accepting a hydroxide ion:

$\mathrm{B(OH)_3 + 2H_2O \rightleftharpoons [B(OH)_4]^- + H_3O^+}$

The proton is released from water, not directly from boric acid. So boric acid is not a protonic acid.

Hence, A is false.

Check option B: Beryllium exhibits coordination number of six

Beryllium is a very small atom and generally shows maximum covalency/coordination number of 4, for example in complexes like $[\mathrm{BeF_4}]^{2-}$.

Due to the absence of available $d$-orbitals in the valence shell and its small size, coordination number 6 is not typical for beryllium.

Hence, B is false.

Check option C: Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase

• Beryllium chloride $\mathrm{BeCl_2}$ is covalent and in solid state has a polymeric bridged structure with chlorine bridges.
• Aluminium chloride $\mathrm{AlCl_3}$ is also electron-deficient and in solid state exists with bridged chloride linkage (dimeric/polymeric association depending on phase; $\mathrm{Al_2Cl_6}$ with Cl bridges is well known).

Therefore, the statement is correct.

Hence, C is true.

Check option D: $B_2H_6\cdot 2NH_3$ is known as ‘inorganic benzene’

“Inorganic benzene” refers to borazine, $\mathrm{B_3N_3H_6}$, not $\mathrm{B_2H_6\cdot 2NH_3}$.

Hence, D is false.

Final conclusion

The only correct statement is:

$\boxed{\text{C}}$

Comparison with stored correct answer

Stored correct answer = C

My derived answer = C

So, the answers agree.