A balanced chemical equation gives quantitative ratios among the amounts of reactants and products. These relationships are the reaction's stoichiometry.

For

$$\mathrm{N_2+3H_2\rightarrow2NH_3},$$

the coefficients imply

$$1\ \mathrm{mol\ N_2}:3\ \mathrm{mol\ H_2}:2\ \mathrm{mol\ NH_3}.$$

Any pair of coefficients can therefore be written as a stoichiometric factor, for example

$$\frac{2\ \mathrm{mol\ NH_3}}{1\ \mathrm{mol\ N_2}}$$

or its reciprocal. The useful orientation is the one that cancels the amount unit of the known species and leaves the desired species.

Suppose $14.0,\mathrm g$ of nitrogen reacts with excess hydrogen. Using $M_{N_2}=28.02,\mathrm{g/mol}$ and $M_{NH_3}=17.03,\mathrm{g/mol}$,

$$14.0,\mathrm g\ N_2 \times\frac{1,\mathrm{mol\ N_2}}{28.02,\mathrm g\ N_2} \times\frac{2,\mathrm{mol\ NH_3}}{1,\mathrm{mol\ N_2}} \times\frac{17.03,\mathrm g\ NH_3}{1,\mathrm{mol\ NH_3}} \approx17.0,\mathrm g\ NH_3.$$

The mole is the bridge: masses of different substances are not normally related by the raw equation coefficients because different species have different molar masses.

Stoichiometric factors describe proportional amounts if the stated reaction occurs according to the balanced equation. They do not by themselves say whether enough of every reactant is present, whether the reaction reaches completion, or how much product is actually recovered.