Spin-only magnetic moment of Mn in KMnO$_4$:
\[\mu = 0\]
Spin-only magnetic moment of the manganese product formed during titration of KMnO$_4$ against oxalic acid in acidic medium:
\[\mu = 6 \, \text{BM}\]
Difference in magnetic moments:
\[6 - 0 = 6 \, \text{BM}\]