**Core Concept**
A neuroendocrine tumour (NET) causing biliary obstruction involves a rare but significant clinical scenario. NETs arise from neuroendocrine cells distributed throughout the body, including the pancreas and gastrointestinal tract. Biliary obstruction in this context is often due to the tumor's growth in the pancreas or periampullary region.

**Why the Correct Answer is Right**
The correct answer is **Carcinoid tumor**. Carcinoid tumors are a subset of NETs that can arise in the pancreas or periampullary region, leading to biliary obstruction. They secrete serotonin, which can cause fibrosis and subsequent biliary strictures. The tumor's growth can also lead to bile duct obstruction, resulting in jaundice and other symptoms.

**Why Each Wrong Option is Incorrect**
**Option A:** **Pheochromocytoma** is a type of NET that primarily affects the adrenal glands and is associated with hypertension, not biliary obstruction.

**Option B:** **Pancreatic adenocarcinoma** is a more common cause of biliary obstruction, but it is not a type of neuroendocrine tumor.

**Option D:** **Gastrinoma** is a type of NET that can cause Zollinger-Ellison syndrome, leading to peptic ulcers and diarrhea, but it is not typically associated with biliary obstruction.

**Clinical Pearl / High-Yield Fact**
When considering NETs causing biliary obstruction, remember that carcinoid tumors can lead to fibrosis and biliary strictures due to serotonin secretion, making them a critical consideration in the differential diagnosis.

**Correct Answer:** C. Carcinoid tumor.