When the following chemical reaction is balanced, what number is placed before NH3? N2 + 3H2 → NH3

In the right side You have 2N, so the outcome has also to conclude 2N, because in this case the outcome is only 1 thing you can balance it this way. Though, when number of outcomes icreases it gets harder to guess which one you should balance first. Of course there are other "advanced" methods to do it precisely, but it takes studying. For You doing elementary chemistry You can balance it this way.

A chemical reaction is usually defined a reaction between two or more reactants and thereby producing one or more products out of it. This reactions are needed to be balanced on both the sides by a definite number in order to conserve the mass.

In the given condition, Nitrogen is reacting with Hydrogen in order to form ammonia (NH₃)

N₂ + 3H₂ → 2NH₃

Thus, the above reaction is balanced now by putting 2 before NH₃.