The correct answer is option 4, bone marrow. The bone marrow is responsible for synthesizing red blood cells in the adult human body. Red blood cells, also known as erythrocytes, are crucial for transporting oxygen from the lungs to different tissues and organs throughout the body.

Option 1, the liver, does play a role in the production and breakdown of red blood cells, but it does not synthesize them in the same way that the bone marrow does. The liver primarily produces a component called bilirubin, which is a waste product of red blood cell breakdown.

Option 2, muscles, are not involved in the synthesis of red blood cells. Muscles are responsible for movement and muscle contractions, but they do not have the capability to produce blood cells.

Option 3, the pancreas, has a different function in the body. It is mainly responsible for producing digestive enzymes and regulating blood sugar levels, but it does not synthesize red blood cells.

Therefore, the correct answer is option 4, bone marrow, as it is the primary site for the synthesis of red blood cells in the adult human body.