**Core Concept**
The question tests the understanding of the life cycle of *Plasmodium falciparum*, specifically the stages visible in a peripheral blood smear. *P. falciparum* is a protozoan parasite that causes malaria, and its life cycle includes several stages.

**Why the Correct Answer is Right**
The correct answer includes **ring forms** and **gametocytes**, which are the stages typically seen in the peripheral blood smear of a patient infected with *P. falciparum*. The **ring forms** are the early trophozoite stages of the parasite, while **gametocytes** are the sexual stage of the parasite.

**Why Each Wrong Option is Incorrect**
**Option A:** Schizonts are typically sequestered in the tissues and are not usually seen in the peripheral blood smear.
**Option C:** Accole is not a recognized stage in the life cycle of *P. falciparum*.

**Clinical Pearl / High-Yield Fact**
It's crucial to remember that *P. falciparum* is characterized by the presence of **ring forms** and **gametocytes** in the peripheral blood smear, which aids in its diagnosis.

**Correct Answer:** D. ring forms, gametocytes