To determine which reaction is NOT a redox reaction, we need to analyze each option for changes in oxidation states.$\\$Option 1: $$H$_2 +$Cl$_2 \rightarrow 2$HCl$\\$• In $$H$_2,$the oxidation state of H is 0. In $$HCl$,$the oxidation state of H is +1.$\\$• In $$Cl$_2,$the oxidation state of Cl is 0. In $$HCl$,$the oxidation state of Cl is -1.$\\$This is a redox reaction because there is a change in oxidation states.$\\$Option 2: $$BaCl$_2 +$Na$_2$SO$_4 \rightarrow$BaSO$_4 + 2$NaCl$\\$• In $$BaCl$_2,$the oxidation state of Ba is +2 and Cl is -1.$\\$• In $$Na$_2$SO$_4,$the oxidation state of Na is +1, S is +6, and O is -2.$\\$• In $$BaSO$_4,$the oxidation state of Ba is +2, S is +6, and O is -2.$\\$• In $$NaCl, the oxidation state of Na is +1 and Cl is -1.$\\$There is no change in oxidation states, so this is NOT a redox reaction.$\\$Option 3: $$Zn$+$CuSO$_4 \rightarrow$ZnSO$_4 +$Cu$\\$• In $$Zn, the oxidation state is 0. In $$ZnSO$_4,$the oxidation state of Zn is +2.$\\$• In $$CuSO$_4,$the oxidation state of Cu is +2. In $$Cu, the oxidation state is 0.$\\$This is a redox reaction because there is a change in oxidation states.$\\$Option 4: $2$KClO$_3 \rightarrow 2$KCl$+ 3$O$_2 \\$• In $$KClO$_3,$the oxidation state of Cl is +5.$\\$• In $$KCl, the oxidation state of Cl is -1.$\\$• Oxygen is reduced from -2 in $$KClO$_3$ to 0 in $$O$_2. \\$This is a redox reaction because there is a change in oxidation states.$\\$Therefore, the reaction that is NOT a redox reaction is Option 2: $$BaCl$_2 +$Na$_2$SO$_4 \rightarrow$BaSO$_4 + 2$NaCl.