And #"iodide"# is oxidized to #"triiodide"#.............
#"Reduction:"#
#ClO^(-) +2H^(+) + 2e^(-) rarrCl^(-) + H_2O# #(i)#, yes I know you asked for basic solution, but attend........
#"Oxidation:"#
#3I^(-) rarrI_3^(-) + 2e^(-)# #(ii)#
For each half equation, mass and charge are conserved as is required. Am I right?
We add #(i)# and #(ii)# to remove the electrons.
#ClO^(-) +2H^(+) + 3I^(-) rarrI_3^(-) + Cl^(-) +H_2O#
But you specified basic solution. So all we have to do is add #2xxHO^-# to each side:
#ClO^(-) +cancel2H_2O(l) + 3I^(-) rarrI_3^(-) + + Cl^(-) +2HO^(-)+cancel(H_2O)#
To give me finally,
#ClO^(-) +H_2O(l) + 3I^(-)rarrI_3^(-) + Cl^(-) + 2HO^(-)#
Which I think is balanced with respect to mass and charge.