Write a balanced chemical equation for the synthesis of ammonia from hydrogen and nitrogen gas

Thas is the famous Haber process.

The chemical equation of the reaction involved is:

⇄    <-------- answer

As you see it is an equillibrium reaction where 4 molecules of reactants form 2 molecules of product.

The balance is checked in this way

                   Reactants           Products
                    # of atoms          # of atoms

Element

N                  2                         2 * 1 = 2 => check

H                  3*2 = 6                2 * 3 = 6 => check

The number of atoms of each element is the same on both sides, which is what balancing is about.