Write the balanced chemical equation for the reverse reaction. include physical states for all species.

The balanced equation for the reverse reaction would be

Reversible reactions

They are reactions that proceed in opposing directions - that is, reactants to products and vice versa.

The equilibrium system between sulfur dioxide gas, oxygen gas, and sulfur trioxide gas can be represented as:

Thus, the reverse reaction would be:

More on equilibrium reactions can be found here: link

The equilibrium system between sulfur dioxide gas, oxygen gas, and sulfur trioxide gas is given. Write the balanced chemical equation for the reverse reaction. Include physical states for all species.

This is a missing part of your question:
The equilibrium system between sulfur dioxide gas, oxygen gas, and sulfur trioxide gas is given.
So you need the equilibrium balanced equation of SO2, O2, SO3 reaction:
First, we will start with the original equation which is not balanced yet (to understand how we get it):
SO2 + O2 ↔ SO3 
Here the number of O atom is not equal at the to sides
So we will start to balance our equation by make the number of O atom equal each other on both sides:
So we will start to put 2SO3 instead of SO3 
and put 2SO2 instead of SO2 to balance also the S atom on both sides
So we will get this:
2SO2(g) + O2(g) ↔ 2SO3(g) (This is our equilibrium balanced equation)
know we have a number of O atom equals on each side = 6
and the sulfur equals on each side = 2