Assign the oxidation number to all the elements in the reaction,

$2{\stackrel{+5}{\mathrm{I}}{\mathrm{O}}_3}^{-}+\mathrm{x}\stackrel{-1}{{\mathrm{I}}^{-}}+12\stackrel{+1}{{\mathrm{H}}^{+}}\to 6\stackrel{0}{{\mathrm{I}}_2}+6{\mathrm{H}}_2\mathrm{O}$

$2{\mathrm{IO}}_3^{-}+10{\mathrm{e}}^{-}\to {\mathrm{I}}_2$

$\left[2{\mathrm{I}}^{-}\to {\mathrm{I}}_2+2{\mathrm{e}}^{-}\right]\times 5$

$2{\mathrm{IO}}_3^{-}+10{\mathrm{I}}^{-}+12{\mathrm{H}}^{+}\to 6{\mathrm{I}}_2+6{\mathrm{H}}_2\mathrm{O}$

Therefore, the value of  $\mathrm{x}=10$ in the reaction.