To balance a chemical equation, stoichiometric coefficients must be added to the reactants and products in such a way that the number of atoms of each element on both sides is the same, or that the number of atoms in reactants and products are equal. The steps listed below can be used to balance equations:
1. If the chemical formula is not provided, write it first. However, in this situation, the chemical formula is provided, therefore write the imbalanced reaction first.

$\mathrm{Fe}{\left({\mathrm{NO}}_3\right)}_3+\mathrm{KSCN}\to \mathrm{Fe}(\mathrm{SCN}{)}_3+{\mathrm{KNO}}_3$

2. Next, compare the total number of each element on both sides. For example, in the given reaction, there is one F e atom and one K atom on both sides, but there are different numbers of $N{O}_3$and S C N atoms on each side. On the reactant side, there are three ${\mathrm{NO}}_3$ atoms and one SCN atom, whereas on the product side, there is only one ${\mathrm{NO}}_3$.

3. Next, stoichiometric coefficients are added to molecules containing an element that differ in the number of atoms on the reactant and product sides. The coefficients are added in a way that balances the equation, and then the equation is checked to see if the number of atoms is the same on both sides or not.
Consequently, the balanced equation for the given equations can be expressed as follows:

$\mathrm{Fe}{\left({\mathrm{NO}}_3\right)}_3+3{\mathrm{KSCN}}_3\to \mathrm{Fe}(\mathrm{SCN}{)}_3+3{\mathrm{KNO}}_3$

Hence, option B is correct.