Why following two reaction proced differently?
`Pb_(3)O_(4)+8HClrarr3PbCl_(2)+Cl_(2)+4H_(2)O`
and
`Pb_(3)O_(4)+4HNO_(3)rarr2Pb(NO_(3))_(2)+PbO_(2)+2H_(2)O`

Explanation

`Pb_(3)O_(4)` is a mixed oxide of `(PbO_(2)+2PbO)`. In `PbO_(2), Pb` is in `+4` oxidation state and the stable oxidation state of `Pb` in `PbO is +2`. `PbO_(2)` thus acts as an oxidising agent (oxidant) and therefore can oxidise `Cl^(ө)` ion of `HCl` into `Cl_(2)`. Moreover, `PbO` is a basic oxide.
Thus, the reaction
`Pb_(3)O_(4)+8HClrarr3PbCl_(2)+Cl_(2)+4H_(2)O`
is split into two reactions as follows:
`2PbO+4HClrarr2PbCl_(2)+2H_(2)O` (acid base reaction)
`overset(+)PbO_(2)+4Hoverset(-1)Clrarroverset(+2)PbCl_(2)+Cl_(2)+2H_(2)O` (redox reaction)
Reaction between `PbO_(2)` and `HNO_(3)` does not occur since `HNO_(3)` is itself an oxidising agent but the acid base reaction between `PbO` and `HNO_(3)` occurs as follows:
`2PbO+4HNO_(3)rarr2Pb(NO_(3))_(2)+2H_(2)O`
`PbO_(2)` is passive against `HNO_(3)`. That is why the reaction proceeds differently with `HCl`