**Core Concept**
Amoebiasis is a parasitic infection caused by Entamoeba histolytica, which can manifest in both intestinal and extra-intestinal sites. The extra-intestinal manifestations of amoebiasis are often a result of the hematogenous spread of the amoeba from the intestinal tract.

**Why the Correct Answer is Right**
The most common extra-intestinal manifestation of amoebiasis is pulmonary amoebiasis, which occurs when the amoeba enters the bloodstream and lodges in the lungs. This can lead to symptoms such as cough, chest pain, and shortness of breath. The amoeba can also cause a range of other extra-intestinal manifestations, including liver abscesses, pericarditis, and meningitis.

**Why Each Wrong Option is Incorrect**
**Option A:** Intestinal obstruction is a complication of amoebiasis, but it is not an extra-intestinal manifestation.
**Option B:** Liver abscess is a possible complication of amoebiasis, but it is not the most common extra-intestinal manifestation.
**Option C:** Cutaneous amoebiasis is a rare manifestation of the disease and not the most common extra-intestinal manifestation.

**Clinical Pearl / High-Yield Fact**
Amoebiasis can present with a range of symptoms, including diarrhea, abdominal pain, and weight loss, but it is often asymptomatic in its early stages. A high index of suspicion is required to diagnose the disease, particularly in patients with a history of travel to endemic areas or exposure to contaminated food and water.

**Correct Answer:** B. Liver abscess is a possible complication of amoebiasis, but it is not the most common extra-intestinal manifestation.