**Core Concept**
The most common side-effect of chemotherapy administration is related to the body's response to the release of various chemical mediators and cytokines that are released in response to the damage caused by the chemotherapeutic agents. This results in a systemic inflammatory response, leading to symptoms that are similar to those seen in infections.

**Why the Correct Answer is Right**
The correct answer is **nausea and vomiting**. This occurs due to the stimulation of the chemoreceptor trigger zone (CTZ) in the area postrema of the brain, which is sensitive to chemical changes in the cerebrospinal fluid. Chemotherapy agents such as cisplatin, doxorubicin, and etoposide can cause a release of serotonin, dopamine, and other neurotransmitters that stimulate the CTZ, leading to nausea and vomiting. Other mechanisms, such as the release of cytokines and the activation of the hypothalamic-pituitary-adrenal axis, also contribute to the development of chemotherapy-induced nausea and vomiting (CINV).

**Why Each Wrong Option is Incorrect**
**Option A:** While fatigue is a common side-effect of chemotherapy, it is not the most common side-effect. Fatigue occurs due to the anemia, bone marrow suppression, and the direct toxic effects of chemotherapy agents on tissues.
**Option B:** Alopecia (hair loss) is a common side-effect of chemotherapy, but it is not the most common. Alopecia occurs due to the damage of hair follicles by chemotherapy agents.
**Option C:** Diarrhea can occur as a side-effect of chemotherapy, but it is not the most common. Diarrhea occurs due to the damage of the gastrointestinal mucosa and the disruption of the normal intestinal flora.

**Clinical Pearl / High-Yield Fact**
Chemotherapy-induced nausea and vomiting (CINV) can be classified into two types: acute and delayed. Acute CINV typically occurs within 24 hours of chemotherapy administration, while delayed CINV occurs 24-48 hours after chemotherapy.

**Correct Answer:** D. Nausea and vomiting.