Can 2% hydroquinone be as effective as 4% just over a longer period of time, or is it not possible to ever see the same results? treating dark circles

In general: the higher percentage concentration will be more effective ... you can't really make up effectiveness with a lower concentration applied over a longer period of time. I understand the 2% strength is available over the counter without a prescription which is probably the basis for your question. The higher 4% strength will be available by prescription; consider making an appointment.