What are the physical states of this products CaCl2 (aq) + NaCO3 (aq) → CaCO3+ NaCl2?

Since both reactants are aqueous they are in the presence of water. Therefore, if the products are soluble in water, they will also be aqueous. According to solubility rules, NaCl is aqueous while most carbonates are not. Therefore, it should be NaCl(aq) and CaCO3(s).
aq means in aqueous solution NB I think your reactant should be Na2CO3 and product 2NaCl for valency.
CaCo3 is solid and I would have thought that NaCl should also be aqueous (it is common salt after all!)
CaCO3 is a solid (precipitate).
NaCl is aqueous ('aq').
Well first of all you have a wrong equation, the reactant should be Na2CO3 since carbonate is an anion with -2 charge; The NaCl2 product will never exist; replace it with 2NaCl

Now on to the states- I do believe CaCO3 will precipitate (become a solid) while NaCl is always aqueous.

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