what are redox/non-redox not getting it? Can you break it down?

NaOH + HCl ==> NaCl + H2O is a non-redox equation. Specifically it i an acid/base equation. But you see I have 1 Na, 1 O, 1 Cl, an 2H atoms on each side.

KMnO4 + 5FeCl2 + 8HCl ==> 5FeCl3 + MnCl2 + 4H2O + KCl

You see I have 1 K, 1 Mn, 4 O, 5 Fe, and 18 Cl atoms on each side.
The first I balanced by trial and error. The second one I followed rules.
Here is a site that can help with redox equations.
http://www.chemteam.info/Redox/Redox.html