Final answer:
Nursing students show understanding of active euthanasia by identifying the injection of an excessive insulin dose as an example, as it entails a direct action to end a patient's life(option b).
Step-by-step explanation:
The nursing students demonstrate understanding of active euthanasia when they identify deliberately injecting an excessive insulin dose as an example. This scenario describes a direct action taken to end the life of a patient, which aligns with the definition of active euthanasia. Active euthanasia involves intentional medical intervention to terminate a patient's life, such as administering a lethal dose of medication. In contrast, extubating a mechanically ventilated client, providing analgesia that produces light sedation, and writing a prescription for barbiturates can all be related to palliative care or passive euthanasia and do not directly cause the death of the patient.
It's important to note that active euthanasia remains a legally sensitive issue and is illegal in the United States, but in the context of the question, the example of injecting an excessive insulin dose most accurately represents active euthanasia.
Hence, the answer is option b.