Here the reacting species are zinc (Zn) and iron III chloride, which can be written as FeCl3. Since this is a single replacement reaction, we can expect that zinc will replace iron (III). Such a single replacement reaction will produce zinc chloride and iron (III). The chemical reaction for this case can be written as
Zn + FeCl3 -> ZnCl2 + Fe.
For a balanced reaction, the number of atoms of each chemical species should be equal on both sides of a chemical reaction. Let's start with each species.
For zinc, the reactant side contains 1 atom and the product side also contains 1 atom. Similarly, for iron (III), there is 1 atom each on the reactant and the product side. For chlorine, the reactant side contains 3 atoms, while the product side has only 2 atoms.
Hence this equation is not balanced for chlorine atoms.
To balance chlorine, let's multiply FeCl3 by 2 and ZnCl2 by 3, so as to have 6 atoms (2 x 3 on the reactant side and 3 x 2 on the product side) of chlorine on each side of the equation.
We get Zn + 2 FeCl3 -> 3ZnCl2 + Fe.
Now, the equation is balanced for chlorine, but not for zinc or iron. To balance for zinc, let's multiply the zinc on the reactant side with 3. Similarly to balance iron, we need to multiply the iron on the product side with 2.
We get 3Zn + 2FeCl3 -> 3ZnCl2 + 2Fe.
Now, we can check and see that all the atoms are equal in number on both sides of the equation, and hence this is our balanced chemical reaction for the given case.
Hope this helps.