In an oxidation-reduction reaction there is an exchange of electrons.
The exchange of electrons implies change in the oxidation states: at least one element increases its oxidation number while other reduces it.
By simple ispection you can predict that in the equation b. there is a change in oxidation states of Cl and Mn.
Now you can check it:
Equation 4H Cl + Mn O2 -> Mn Cl2 + 2H2 O + Cl2
oxidation sates 1+ 1- 4+ 2- 2+ 1- 1+ 2- 0
The oxidation state of Cl in HCl is 1- and it changed to 0 in Cl2
The oxidation state of Mn in MnO2 is 4+ and it changed to 2+ in MnCl2
Answer b.
