Step 1: Understand the question.
We need the catalyst that helps add hydrogen to ethene (turning ethene into ethane).
Step 2: Recall the reaction.
Hydrogenation adds $\text{H}_2$ across the double bond: \[ \text{CH}_2\text{=CH}_2 + \text{H}_2 \xrightarrow{\text{catalyst}} \text{CH}_3\text{-CH}_3 \]
Step 3: Recall why a catalyst is needed.
Hydrogen gas is sluggish on its own, so a metal surface is used to grab and split the $\text{H}_2$ molecules so they can react.
Step 4: List the metals that do this.
Nickel, palladium and platinum are the usual hydrogenation metals. Finely divided nickel gives a large surface and works well at mild heat.
Step 5: Rule out the others.
$\text{MnO}_2$ is used to break down hydrogen peroxide, and iron is the catalyst for making ammonia, so neither fits hydrogenation of ethene.
Step 6: Pick the answer.
The catalyst is finely divided nickel, option (C).
\[ \boxed{\text{Ni (finely divided)}} \]