The reaction Pb(NO$$_3$$)$$_2$$ and NaCl in water produces a precipitate that dissolves upon the addition of HCl of appropriate concentration. The dissolution of the precipitate is due to the formation of

The aqueous double-displacement reaction between lead(II) nitrate and sodium chloride is

$$Pb(NO_3)_2 \;+\; 2\,NaCl \;\rightarrow\; PbCl_2\,(s)\;+\;2\,NaNO_3$$

Lead(II) chloride, $$PbCl_2$$, is sparingly soluble, so a white precipitate appears.

When concentrated hydrochloric acid (or any source of high $$Cl^-$$ concentration) is added, the precipitate gradually disappears because $$Pb^{2+}$$ ions form a soluble chloro-complex with excess chloride ions. Complex-ion formation shifts the solubility equilibrium according to Le Châtelier’s principle.

The stepwise complex-formation equilibria are

$$Pb^{2+} + 2\,Cl^- \;\rightleftharpoons\; PbCl_2\,(s)$$
$$PbCl_2\,(s) + 2\,Cl^- \;\rightleftharpoons\; [PbCl_4]^{2-}$$

Because the formation constant $$K_f$$ for $$[PbCl_4]^{2-}$$ is large, the second reaction proceeds to the right in the presence of excess $$Cl^-$$, converting the insoluble solid into the soluble tetra­chloroplumbate(II) ion.

Other species listed in the options are either the original precipitate (Option A), an unstable covalent molecule $$PbCl_4$$ (Option B) which would require oxidation of lead(II) to lead(IV), or an octahedral complex $$[PbCl_6]^{2-}$$ (Option D) that is not formed under these conditions. Experimental evidence and stability-constant data confirm that $$[PbCl_4]^{2-}$$ is the dominant chloro-complex of Pb(II) in concentrated chloride media.

Hence, the dissolution of the $$PbCl_2$$ precipitate is due to the formation of the soluble complex ion $$[PbCl_4]^{2-}$$.

Option C which is: $$[PbCl_4]^{2-}$$