How to balance the reaction equation of potassium permanganate, calcium oxalate, and sulfuric acid step by step?
This is a redox reaction. While it can be balanced by the method you describe, it is much more reliable to balance it by the half-reaction method.

Step 1 - Identify your spectator ions (so we do not spend time trying to balance them)

Three ions appear unchanged on both sides of the reaction: $\ce{K+},\ \ce{Ca^2+},\ \&amp; \ \ce{SO4^2-}$

Step 2 - Identify your redox pairs.

You have one manganese species on each side. They must constitute one half-reaction:
$$\ce{MnO4- -&gt; Mn^2+}$$
Likewise, you have on carbon species on each side. They must constitute the other half reaction:
$$\ce{C2O4^2- -&gt; CO2}$$
For each half reaction:

Step 3 - Balance O by adding $\ce{H2O}$
Step 4 - Balance H by adding $\ce{H+}$
Step 5 - Balance charge by adding $\ce{e-}$
Step 6 - Combine the half reactions

Can you take it from here?