For this question, we're given a reduction-oxidation (redox) reaction. We're asked to identify an answer choice that correctly states what the reducing agent is and what the oxidizing agent is.

Notice that another way we can write this reaction is by breaking up the ions as if they were dissociated in solution.

Notice in the above example that the potassium ion remains in the same oxidation state. This is what is known as a spectator ion, meaning that it doesn't really participate in the reaction and remains unchanged on reactant and product sides of the equation. Hence, we can remove it from both sides to simplify things.

In the simplified reaction shown above, we can see that the chlorine element is being reduced, while the iodine is being oxidized. Since the chlorine is being reduced, the iodine must be acting as the agent responsible for this. Hence, the is the reducing agent. Moreover, since the iodine is being oxidized, the chlorine must be the agent responsible for this. Thus,  is the oxidizing agent.

Remember that the  we're referring to as the reducing agent is originally in the form of , which we can thus state as the reducing agent in the overall, unsimplified reaction.

A reducing agent is the compound in the reactants which becomes oxidized.

Oxidation is defined as the loss of electrons and is shown by the element changing to have a more positive oxidation number in the reaction.

To determine the reducing agent we simply see which compound is oxidized by determining the oxidation numbers of the elements in both the reactants and products, and comparing them.

Reactants:

For  its oxidation state is simply zero because the oxidation number of an atom in its elemental form is always zero.

Same goes , which is why its oxidation number is also zero.

Products:

 has a charge of , so its oxidation number is .

 has a charge of , so its oxidation number is 

Results:

Since  loses electrons it is oxidized and therefore its the reducing agent. 

None of the products can be the reducing agent because this reaction isn't reversible.

The reducing agent is the compound which contains the element being oxidized. Oxidation is defined as the loss of electrons, so the element which is oxidized becomes more positively charged.

In order to determine which element is oxidized we need to calculate the oxidation numbers of all the elements in the reactants and products and compare them. The element which has an oxidation number that increases overall is the one that is oxidized. We determine the oxidation numbers by applying the elementary rules of oxidation numbers to each compound.

For reference the chemical equation is:

Let's start with the reactants:

 because a rule of oxidation states is that oxidation number of all halogens is generally .

 for the same reason as bromine.

 because  is neutrally charged and bromine has a charge of  and there are two bromines, so in order for the compound to maintain a neutral charge iron must have a charge of .

 for the same why iron is, except in this case it is due to chlorine's  charge instead of bromine.

Products:

 because the oxidation number of all halogens is generally .

 for the same reason as bromine.

 and  because they both must be numbers that allow each of their respective compounds to be neutrally charged. For the same reasoning as in the reactants they both must be .

Since there are no changes in the oxidation numbers of any of these elements, this isn't a redox reaction therefore there is no reducing agent.

The oxidizing agent is the compound which contains the element being reduced. Reduction is defined as gaining of electrons, so the element which is reduced becomes more negatively charged.

In order to determine which element is reduced we need to calculate the oxidation numbers of all the elements in the reactants and products and compare them. The element which has an oxidation number that decreases overall is the one that is reduced and therefore the oxidizing agent. We determine the oxidation numbers by applying the elementary rules of oxidation numbers to each compound.

For reference the chemical equation is:

Let's start with the reactants:

 because it is in the same group as oxygen which by the general rules of oxidation numbers has a charge of . Although sulfur can assume other oxidation numbers, it is also  in this particular case because chromium is a transition metal that prefers to lose electrons to become more stable (become more positively charged) and since sulfur has a greater electronegativity it prefers a negatively charged state in this case.

 because sulfur is  and since  is a neutral compound chromium must be 

 because a general rule of oxidation numbers is that oxygen usually has an oxidation number of .

In order to determine what phosphorus is we must look at the phosphate ion . Phosphate is an anion which has a charge of  and in order for that to be possible with four oxygens () P must have a charge of .

= because the phosphate anion has a charge of , so  must offset that charge for  to be neutrally charged. 

Products:

 for the same reason it is in the reactants, except because  is the transition metal in this case which prefers to lose electrons.

 because  is neutrally charged, so it must offset the charge of .

 for the same reason as in the reactants

 for the same reason in the reactants

 to offset the  charge of the phosphate compound it is attached to.

Now let's compare the oxidation numbers of each element:

Oxygen, phosphate, and sulfur have the same oxidation states in both products and reactants.

Chromium increases from an oxidation state of  to .

Finally, manganese decreases from an oxidation state of  to , so it is the compound which is reduced because it gains electrons. Therefore the compound containing manganese is the oxidizing agent. This compound is , which is the right answer.