Final answer:
The most likely cause of cyanosis in a child with a 6 year history of a VSD is Eisenmenger syndrome.
Step-by-step explanation:
Cyanosis is a bluish discoloration of the skin due to low levels of oxygen in the blood. In the case of a child with a 6 year history of a Ventricular Septal Defect (VSD) becoming profoundly cyanotic, the most likely cause is Eisenmenger syndrome. Eisenmenger syndrome is a complication of a VSD where blood from the left ventricle flows back into the right ventricle due to increased pressure in the lungs. This causes oxygenated and deoxygenated blood to mix, resulting in cyanosis.