Let us look at the half reactions i.e. oxidation and reduction separately.
Oxidation:
S8→S2O2−3
S8+24OH−→4S2O2−3+12H2O+16e−….(1)
Reduction:
S8→S2−
S8+16e−→8S2− .......(2)
Adding both the reactions (1) and (2),
2S8+24OH−→4S2O2−3+8S2−+12H2O
Dividing the whole equation by 2,
S8+12OH−→2S2O2−3+4S2−+6H2O
So, c = 4