Step 1 - Understanding the names of the substances as well as the physical states
In the description of the reaction:
“Aqueous calcium hydroxide reacts with carbon dioxide gas to produce solid calcium carbonate and liquid water."
Let's note two things: first, that the name of the substance is given; second, that the physical state, in bold, is as important as its name.
Aqueous calcium hydroxide means that the substance calcium hydroxide is dissolved in water, which is represented by (aq) bellow the substance. Other physical states, such as gas, solid and liquid can be represented in the same way by (g), (s) and (l), respectively.
We know the reactants are calcium hydroxide, Ca(OH)2, and carbon dioxide, CO2. The products are calcium carbonate, CaCO3, and water, H2O.
We don't need to know exactly what is calcium hydroxide and calcium carbonate, given that we know the formulas of CO2 and H2O and also know the physical state of the substances. Mathing both things will give us the correct chemical equation.
Step 2 - Finding the correct chemical equation
As we saw in the previous step, we expect to find:
Let's look at the equations:
Item a can't be the correct answer, since we have formed an aqueous substance, not a solid one.
Item b can't be the correct answer as well, because water, H2O, is a product in the reaction, not a reactant.
Item c is the correct answer. Note that it satisfies all the conditions we have previously established: CO2 in the reactants, H2O in the products; an aqueous reactant and a solid product.