3Fe(s) + 4H2O(g) <-> Fe3O4(s) + 4H2(g)
What happens when Fe(s) is added?
Would the reaction shift right?
I wonder why your teacher gave you this reaction. It is the wrong reaction to discuss LeChantlier's principle.
If the Fe was in solution, yes it would shift to the right. However, the reaction is not reversible so showing it as an equilibrium reaction is very very misleading.
Second point: the Fe is not in solution, and in fact you could add 45 tons of it, and the reaction would not shift right or left, because solids are NOT a factor in equilibrium.
In this reaction
keq=[H2]^4 / [H2O(g)]^4
notice no Fe(s), nor Fe3O4 is a factor in equilibrium.
So all this maybe interesting, but I wonder if your teacher made this up, what was he thinking about? Maybe he wanted you to surmise what I stated, no effect, but few beginning students would ever see that.
LeChatelier's principle holds for equilibrium reactions, but in this case, this is the wrong teaching example.
The changes reacts
To determine whether the reaction would shift to the right when Fe(s) is added, we need to analyze the reaction in terms of Le Chatelier's principle.
In this reaction, Fe(s) (iron) is being introduced. The reaction you provided is a representation of the reaction between iron and water vapor.
According to Le Chatelier's principle, if we add more of a reactant to a system, the reaction tends to shift in the direction that consumes that reactant to achieve a new equilibrium.
In this case, adding more Fe(s) would increase the concentration of iron, which would cause the reaction to shift to the right in order to consume the excess iron.
Therefore, the reaction would indeed shift to the right if Fe(s) is added.