Final answer:
The AX2E2 molecule has a total of four electron domains, consisting of two bonding pairs and two lone pairs.
Step-by-step explanation:
The molecule with the molecular formula AX2E2 is understood in terms of VSEPR theory, which helps predict the shape of molecules. The notation AX2E2 indicates a central atom A with two attached atoms X, and two lone pairs of electrons E. Each X represents a bonding domain (since it's a bond with another atom), and each E represents a nonbonding domain (lone pair). Therefore, the total number of electron domains for an AX2E2 molecule is four: two bonding domains and two nonbonding domains.