Final answer:
The next step should be to administer adenosine 12 mg IV, following ACLS guidelines for a higher dose after an initial lower dose fails to convert SVT, especially since the patient remains hemodynamically stable.
Step-by-step explanation:
The next appropriate intervention for a 45-year-old woman with a history of palpitations, who has developed light-headedness and palpitations and has not converted to a normal rhythm after receiving 6 mg IV adenosine, should be to administer a subsequent dose of adenosine 12 mg IV. This is according to Advanced Cardiovascular Life Support (ACLS) guidelines which recommend a higher dose of adenosine if the initial dose fails to convert the supraventricular tachycardia (SVT).
Performing synchronized cardioversion could be considered in the case of hemodynamic instability, but given the patient's blood pressure is stable, it may not be the immediate next step. Performing vagal maneuvers can precede drug therapy or can be attempted while awaiting drug effects, but it appears these may have already been attempted or deemed inappropriate given her extreme apprehensiveness. As she remains hemodynamically stable, unsynchronized cardioversion is not indicated because it is generally reserved for life-threatening arrhythmias where immediate response is critical.