J.R. S. answered 11/07/22
Ph.D. University Professor with 10+ years Tutoring Experience
I'll leave phases to you, just as I did in my previous answer to your other question.
ReO4- ==> Re(s) ... reduction half reaction
MnO2 ==> MnO4- ... oxidation half reaction
ReO4- ==> Re(s) + 4H2O ... balanced for Re and O
ReO4- + 8H+ ==> Re(s) + 4H2O ... balanced for Re, O and H using acid (H+)
ReO4- + 8H+ + 7e- ==> Re(s) + 4H2O ... balanced reduction reaction
MnO2 + 2H2O ==> MnO4- ... balanced for Mn and O
MnO2 + 2H2O ==> MnO4- + 4H+ ... balance for Mn, O and H using acid (H+)
MnO2 + 2H2O ==> MnO4- + 4H+ + 3e- ... balanced oxidation reaction
Multiply reduction reaction by 3 and oxidation reaction by 7 to equalize electrons:
3ReO4- + 24H+ + 21e- ==> 3Re(s) + 12H2O
7MnO2 + 14H2O ==> 7MnO4- + 28H+ + 21e-
Add and/or cancel like terms to get:
3ReO4- + 7MnO2 + 2H2O ==> 3Re(s) + 7MnO4- + 4H+ ... BALANCED REDOX EQUATION