Final answer:
The pregnant client's obstetrical history should be recorded as gravida 3, para 0-1-2-0, reflecting three pregnancies, no term births, one abortion, two preterm births, and no living children.
Step-by-step explanation:
When recording a client's obstetrical history, the appropriate way to document her past experiences would be gravida 3, para 0-1-2-0. This reflects that she has been pregnant three times (gravida 3) which includes the current pregnancy. 'Para' is further subdivided into four components representing term births (deliveries after 37 weeks), preterm births (deliveries between 20 and 37 weeks), abortions (spontaneous or induced < 20 weeks), and living children. Since she has had a miscarriage at 8 weeks, that would be recorded as one abortion (para 0-1-0-0). The twin pregnancy resulted in preterm births (para 0-1-2-0) who unfortunately died shortly after birth, which means that she has had no term births, one abortion, two preterm births, and currently no living children (the '0' at the end).