How to find the coefficient of Fe^2+ from ClO3^- + Fe^2+ --> Cl^- + Fe^3+
Do this as two half equations.
Fe^+2 ==> Fe^+3 + e
ClO3^- +6e + 6H^+ ==> Cl^- + 3H2O
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To write an equation, one must balance the electrons lost to the electrons gained; therefore, multiply the first half equation by 6 and the second half equation by 1, then add them. You should end up with
6Fe^+2+ ClO3^- + 6e + 6H^+ --> 6Fe^+3 + Cl^- + 3H2O + 6e
Then cancel the two 6e entries since they appear on both sides.