please check

Write the balanced equation, with the enthalpy component, for the rusting process, given that Hf for iron and oxygen is 0 and Hf for ferric oxide is -826 kJ/mol.

4 Fe (s) + 3 O2 (g) --------> 2 Fe2O3 (s)

You need to add the heat one of three ways.
4 Fe (s) + 3 O2 (g) --------> 2 Fe2O3 (s) + heat or

4 Fe (s) + 3 O2 (g) --------> 2 Fe2O3 (s) delta H = -826 kJ/mol or

4 Fe (s) + 3 O2 (g) --------> 2 Fe2O3 (s) delta H = -3304 kJ

I don't know your teacher's preference

To check if the equation is balanced, you can count the number of each type of atom on both sides of the equation. In this case, we have:

4 Fe (s) + 3 O2 (g) --> 2 Fe2O3 (s)

On the left side, there are 4 iron atoms (Fe) and 6 oxygen atoms (O). On the right side, there are also 4 iron atoms (Fe) and 6 oxygen atoms (O). Since the number of atoms is the same on both sides, the equation is balanced.

To add the enthalpy component, you need to indicate the heat exchange that occurs during the reaction. There are three common ways to represent this:

1) Adding the word "heat" as a product:
4 Fe (s) + 3 O2 (g) --> 2 Fe2O3 (s) + heat

2) Writing the enthalpy change as ΔH (delta H):
4 Fe (s) + 3 O2 (g) --> 2 Fe2O3 (s) ΔH = -826 kJ/mol

3) Writing the enthalpy change as a total value:
4 Fe (s) + 3 O2 (g) --> 2 Fe2O3 (s) ΔH = -3304 kJ

The choice between these three options depends on your teacher's preference or the specific context of the question.