The correct answer is option 4: Small intestine.

Fat is digested in the small intestine. The small intestine is the longest part of the digestive system and plays a crucial role in the digestion and absorption of fat. When we consume dietary fat, it enters the small intestine where it is broken down by pancreatic enzymes such as lipase.

These pancreatic enzymes break down fat molecules into smaller components called fatty acids and glycerol, which can be easily absorbed by the cells lining the small intestine. The small intestine is lined with tiny finger-like structures called villi, which increase the absorption surface area. The fatty acids and glycerol are then absorbed into the bloodstream and transported to different parts of the body where they are used for energy or stored.

It`s important to note that the large intestine primarily absorbs water and electrolytes and helps in the formation of feces, but it does not play a significant role in fat digestion. The spleen is involved in filtering blood and producing certain components of the immune system, it is not directly involved in fat digestion. The mouth is responsible for the initial breakdown of food through chewing but does not play a major role in fat digestion.

In conclusion, fat digestion occurs primarily in the small intestine.