NaI+KMnO 4 ​ +H 2 ​ SO 4 ​ →NaIO 3 ​ +MnSO 4 ​ +H 2 ​ O

Balanced molecular equation:

5 NaI + 6 KMnO4 + 9 H2SO4 → 5 NaIO3 + 6 MnSO4 + 3 K2SO4 + 9 H2O

Brief balancing outline (acidic medium, iodide to iodate with permanganate):

• Oxidation (I- to IO3-): I- + 3 H2O → IO3- + 6 e- + 6 H+
• Reduction (MnO4- to Mn2+): MnO4- + 8 H+ + 5 e- → Mn2+ + 4 H2O
• Multiply to balance electrons: 5 I- + 6 MnO4- + 18 H+ → 5 IO3- + 6 Mn2+ + 9 H2O
• Replace ions with salts: I- from NaI, MnO4- from KMnO4, H+ from H2SO4
• Resulting molecular equation: 5 NaI + 6 KMnO4 + 9 H2SO4 → 5 NaIO3 + 6 MnSO4 + 3 K2SO4 + 9 H2O

If you want, I can show a step-by-step electron-balancing check.