What is the formula of ammonium carbonate?

##("NH"_4)_2"CO"_3##

The important thing to recognize here is the fact that you're dealing with two , one which acts as cation and one which acts as anion.

The name of the cation is always added first to the name of the ionic compound. Likewise, the cation is added first to the compound's chemical formula. In this case, you know that you have ammonium, ##"NH"_4^(+)##, as the cation.

The name of the anion follows the name of the cation. In this case, you know that you have the carbonate ion, ##"CO"_3^(2-)##, as the anion.

Now, notice that the anion carries a ##2-## charge. As you know, must be electrically neutral, meaning that the overall positive charge coming from the cation must be balanced by the overall negative charge coming from the anion.

In this case, you need two ammonium cations to balance the ##2-## charge of the carbonate anion. You will thus have

##2 xx ["NH"_4^(+)]" "## and ##" "1 xx ["CO"_3^(2-)]##

which means that the chemical formula for this compound will be

##("NH"_4)_2"CO"_3 ->## ammonium carbonate