Final answer:
The client's peaceful appearance and increased bloody show suggest that she is in the second stage of labor. This is when the baby is expelled from the uterus, following full cervical dilation achieved in the first stage.
Step-by-step explanation:
The nurse observes that the client appears more peaceful and notes an increase in bloody show. This observation suggests that the client is likely transitioning from the first stage of labor to the second stage of labor. During the first stage, the cervix thins and dilates up to about 10 cm to prepare for the baby's passage. The second stage is characterized by the expulsion of the baby, in which uterine contractions continue and the mother will push, often feeling an intense urge to do so. The increased bloody show is a sign that the cervix is continuing to dilate and the body is progressing towards delivery. Since stage three involves the delivery of the placenta after the birth of the baby and stage four pertains to the postpartum recovery period, and since neither of these stages is accompanied by a peaceful appearance or increased bloody show, the correct stage identified by the nurse would be 'B. second stage'.