In acidic solution, VO_2^+1 is reduced to VO^2+, whereas Mn^2+ is oxidized to MnO_4^-1 .

Given the partial equation
VO_2^+1? +Mn^2+? ---> VO^2+ ? + MnO_4^-1?

What must the coefficients be so that the electrons are balanced?

See your post above.