These are four questions and four answers.
In oxidation-reduction reactions at least one element increase its oxidation state and other (or even the same) reduce its oxidation state.
So, you have to determine, for each reaction if there is a change in the oxidation states of some elements.
1) Chemical equation: FeS(s) + 2HCl(aq) → H₂S(g) + FeCl₂(g)
i) The oxidation state of S in FeS (s) is 2 -, so the oxidation state of Fe is 2 + (the rule is that the sum of the oxidation states in a neutral compound is 0, so 2 - 2 = 0)
ii) In HCl, the oxidation state of Cl is 1- and the oxidation state of H is 1+.
iii) In H₂S(g), the oxidation state of H is 1+, and the oxidation state of S is 2-.
iv) In FeCl₂(g), the oxidation state of Cl is 1- and the oxidation state of Fe is 2-.
Conclusion: none of the elements changed its oxidation state, which means that this is not an oxidation-reduction reaction.
2) Chemical equation: AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃
Compound spieces oxidation state
AgNO₃ Ag 1+
NO₃ 1 -
NaCl Na 1+
Cl 1 -
AgCl Ag 1 +
Cl 1 -
Conclusion: none element changed its oxidation state, so it is not an oxidation-reduction reaction
3) Chemical equation:2C₃H₆(g) + 9O₂(g) → 6CO₂(g) + 6H₂O(g)
You can conclude that the element O changed its oxidation state because on the reactant side it is alone, which means that its oxidation state is 0, while on the product side it is combined with C and H, which means that its oxidation state is 2-.
Conclusion: this is an oxidation-reduction reaction.
4) Chemical equation: Fe₂O₃(s) + 3CO(g) → 2Fe(l) + 3CO₂(g)
Compound element oxidation state
Fe₂O₃(s) Fe 3+
O 2 -
CO(g) C 2+
O 2 -
Fe(l) Fe 0
CO₂(g) C 4+
O 2-
Conclusion: since Fe and C changed their oxidation state, this is an oxidation-reduction reaction.