\[ZnC{O_3}\] is thermally more stable than \[MgC{O_3}\] because:
A.$Mg{(OH)_2}$ exhibits only basic properties while $Zn{(OH)_2}$ is amphoteric
B.Polarising action of $Z{n^{ + 2}}$ with 18-electron configuration on the anion is larger than that of $M{g^{ + 2}}$ with noble gas electron configuration of the same size and charge.
C.Both (a) and (b) are correct
D.None of the above is correct

Hint:In the given question the thermal stability of the carbonates are compared. Now we can although say that the first option though defines correct but that isn’t an appropriate explanation for the given problem. But the second option has both the right statement and it also relates to the thermal capability of the compound.

Complete step by step answer:
In the given question we can observe the processes going through in order to get the right option.
So we have to take both the options into account :
Step $1$ : Option $1$ states that $Mg{(OH)_2}$ exhibits only basic properties while $Zn{(OH)_2}$ is amphoteric.
The given statement however is absolutely correct though that doesn't add up to the relative stability of both the compounds. Therefore the given option despite being correct can’t be the right explanation for the question.
Step $2$ : Option $2$ states that the Polarising action of $Z{n^{ + 2}}$ with 18-electron configuration on the anion is larger than that of $M{g^{ + 2}}$ with noble gas electron configuration and of same size and charge.
Yes we can say that the \[ZnC{O_3}\] is thermally more stable than \[MgC{O_3}\] . This is because of the some factore :
Because of the polarising action of $Zn$ with 18-electron configuration on the anion is larger than that of Mg.
This happens due to the noble-gas electron configuration and of the same size and charge.
According to the principle states that the higher the polarizing power gets, the lattice enthalpy and thermal stability will also get higher.
Therefore we can say that the option is the right explanation.

Hence the correct option is option B.

Note:An amphoteric compound can be defined as a molecule or ion that has the capability to react with both as an acid and as a base. Many metals like copper, zinc, tin, lead, aluminium, and beryllium form amphoteric oxides or hydroxides. \[A{l_2}{O_3}\] is an example of an amphoteric oxide.