At what temperature LPG Gas Freeze?

−187.7 °C below this temperature LGP acts as solid

No

The LPG used to fuel cars is a mixture of propane and butane,and they have different freezing points

There is a pressure factor which is important so you need to be more explicit. At what pressure are you interested in?  And when you say "LPG" what do you mean, exactly (compositionally)? That matters too.  Methane, ethane, propane, and butane do not all freeze at the same temperatures for a given pressure, and the mixtures of such gases are not ideal so concentrations do matter.

Pure propane freezes at about -188 C give or take a bit depending on pressure (the slope of the soil-liquid phase boundary is very steep so T changes little with change in P).  This is probably what you mean by "LPG" although it does not have to.  Methane and ethane freeze at slightly higher temps (still below -180C) and butane at somewhat lower temps (-215C or so) at 1 atmosphere.  Unlikely that any container of LPG will actually be at 1 atmosphere pressure but the pressure effects are relatively small.  Still needs the container to be damn cold.

You know that the propane's boiling point is too low, which is

at -42°C or -44°F. Simultaneously, the LPG freezing point is at

188 °C, which is too lower.

A propane tank get cold in the first place as the result of a process called vaporisation, during which liquid propane turns to gas. This happens at the very low temperature of -43.6°F (-42°C), but well above the liquid propane-LPG freezing point of -306.4°F (-188 °C).

LPG (propane) freezing point is -188 °C (-306.4°F). This would only ever occur under laboratory conditions