**Core Concept**
The fuel value of fat refers to the amount of energy it provides to the body per unit of weight. In the context of metabolism, fat is a crucial energy source, particularly during periods of fasting or when glucose levels are low.

**Why the Correct Answer is Right**
Fat has a higher fuel value compared to carbohydrates and proteins. This is because fat is rich in energy-dense molecules, specifically fatty acids, which are broken down into acetyl-CoA in the mitochondria. Acetyl-CoA then enters the citric acid cycle, generating a significant amount of ATP (adenosine triphosphate) through oxidative phosphorylation. The fuel value of fat is approximately 9 kcal/g, making it an efficient energy source.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is likely incorrect because the fuel value of fat is not 3 kcal/g, which is the approximate fuel value of carbohydrates.
* **Option B:** This option is incorrect because the fuel value of fat is not 6 kcal/g, which is the approximate fuel value of proteins.
* **Option C:** This option is incorrect because the fuel value of fat is not 12 kcal/g, which is an implausibly high value.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the fuel value of fat is higher than that of carbohydrates and proteins, making it a vital energy source during periods of caloric restriction or fasting.

**Correct Answer: C. 9 kcal/g**