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$\ce{3Mg + 2As -> Mg3As2}$ ($10\ \mathrm g$ of $\ce{Mg}$ and $10\ \mathrm g$ of $\ce{As}$)
I don't understand why coefficient doesn't change the amount of substance, here's what I did:
$n_{\ce{Mg}}=3\cdot\frac{10\ \mathrm g}{24.31\ \mathrm{g/mol}}=1.233\ \mathrm{mol}$ of $\ce{Mg}$
But the correct solution is:
$n_{\ce{Mg}}=\frac{10\ \mathrm g}{24.31\ \mathrm{g/mol}}=0.411\ \mathrm{mol}$ of $\ce{Mg}$
When you say number of moles, it is a number to express the number of constituent species (atoms, in this case) in the given substance. It does not have any correlation to where that substance will be used and what will be its 'coefficient' in that reaction.
When you say 10g Mg, you mean 0.411 moles of Mg (and vice versa) irrespective of whatever you are going to do with those 10 grams.
Even if you were to use 10g Mg in a reaction such as $$\ce{ 2Mg + O2 -> 2MgO} $$, you would still have 0.411 moles of Mg as it is still equivalent to 10g. Nothing changes on the basis of the 'coefficient'.
You can further try to look up more information to get a better understanding about 'The Mole Concept' because that is where I think your problem lies.
