You don't really have a question...what you have is a lack of confidence. Your half reactions are correct and you are exactly correct when you say "I think I need to multiply Fe by 2."

Balance the electrons and the rest will follow...

Fe^{2+} + 2e^{-} --> Fe, now multiply this by 2 as you suggested to get:

- 2Fe
^{2+}+ 4e^{-}--> 2Fe

Now we have 4 electrons in the reactant side to balance the four electrons on the product side of:

- Mn --> Mn
^{4+}+ 4e^{-}

Bringing the two equations together gives the balanced equation:

- 2Fe
^{2+}+ 4e^{-}+ Mn --> 2Fe + Mn^{4+}+ 4e^{-} - We can simplify this by eliminating the 4 electrons that appear in the reactant and product sides:

Thus we have:

- 2Fe
^{2+}+ Mn --> 2Fe + Mn^{4+}

Good work. You had the solution...maybe on the next problem you will have more confidence in your solution.

Alex J.

Thank you! Next time I will make sure to have the confidence.01/25/21