Suppose the abstract number objects exist.
The abstract object 9 has an essence (what it is) that isn't identical to its existence (that it is). If 9's essence is not identical to its existence, 9's essence is really distinct from its existence (Thomism's claim). Hence, the essence of the abstract object 9 is really distinct from its existence. Then you're off on the second part of the Third Way.
Most Thomists deny the existence of abstract objects, though.