Let me answer with a question: what other number of electrons do you propose, and what is the logic behind the other number?
Well the oxidation state of Cr in Cr2O7(2-) is 6 and the oxidation state of Cr in Cr3+ is obviously 3. So therefore there is a reduction of 3 so there is three electrons. That was my first way of doing it.
With that not been right I tried balancing the charges. So there is 14 +'s and a 2- which equals 12, so that would mean 12 electrons to balance. But that's incorrect.
Well the oxidation state of Cr in Cr2O7(2-) is 6 and the oxidation state of Cr in Cr3+ is obviously 3. So therefore there is a reduction of 3 so there is three electrons. That was my first way of doing it.
With that not been right I tried balancing the charges. So there is 14 +'s and a 2- which equals 12, so that would mean 12 electrons to balance. But that's incorrect.
Product is 2Cr3+, not just Cr3+. 2 x 3 electrons = 6.
Sum of reactants charges minus sum of products charges = 0
Charge is a conserved quantity, so charge of the products must be identical to the charge of the reactants.
Well the oxidation state of Cr in Cr2O7(2-) is 6 and the oxidation state of Cr in Cr3+ is obviously 3. So therefore there is a reduction of 3 so there is three electrons. That was my first way of doing it.
Dead End Street already addressed it, but I will reiterate: oxidation number goes from +6 to +3, so yes, it means reduction consuming three electrons PER REDUCED ATOM. But there are two Cr atoms both in the dichromate anion, and in the products, and each of them requires 3 electrons, so there are 6 electrons consumed per each dichromate anion.