**Core Concept**
The Major Histocompatibility Complex (MHC) is a group of genes crucial for the immune system, particularly in the context of antigen presentation and recognition. MHC genes are divided into three main classes: Class I, Class II, and Class III, each with distinct functions and encoded proteins.

**Why the Correct Answer is Right**
Class III MHC genes encode proteins such as complement components (C2 and C4), heat shock proteins, and cytokines like tumor necrosis factor-alpha (TNF-alpha). These proteins play a role in the immune response and inflammation but are not directly involved in antigen presentation like Class I and II MHC molecules. Therefore, statement D, "Class III does not encode complement," is incorrect because Class III MHC genes indeed encode complement proteins.

**Why Each Wrong Option is Incorrect**
**Option A:** Chromosome six is indeed the location of the MHC complex, which includes genes for Class I and Class II MHC molecules, as well as Class III genes. This statement is correct, not incorrect.
**Option B:** Genes encoding complement proteins are actually located within the Class III region of the MHC complex, not adjacent to Class I. This statement is incorrect because it misplaces the location of complement genes.
**Option C:** Monocytes do express MHC II antigens on their surface, which is a key feature of antigen-presenting cells (APCs). This statement is correct, not incorrect.

**Clinical Pearl / High-Yield Fact**
MHC molecules play a critical role in transplant rejection and autoimmune diseases, such as rheumatoid arthritis and multiple sclerosis. Understanding the different classes of MHC molecules and their functions is essential for immunologists and clinicians dealing with these conditions.

**✓ Correct Answer: D. Class III does not encode complement**