**Core Concept**
Fatty acid synthesis is a crucial anabolic process in which acetyl-CoA units are combined to form long-chain fatty acids. This process is essential for the production of fatty acids, which are vital components of various biomolecules, including triglycerides, phospholipids, and cholesterol.

**Why the Correct Answer is Right**
Fatty acid synthesis occurs in the cytoplasm of cells, specifically in a complex known as fatty acid synthase (FAS). This enzyme complex is composed of multiple subunits, each with a distinct function in the synthesis process. The FAS complex catalyzes the sequential addition of two-carbon units to elongate the fatty acid chain, ultimately resulting in the production of a long-chain fatty acid. The process is tightly regulated by various factors, including the availability of acetyl-CoA, NADPH, and ATP.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because fatty acid synthesis does not primarily occur in the mitochondria. While the mitochondria are involved in fatty acid oxidation, the synthesis process takes place in the cytoplasm.

**Option B:** This option is incorrect because the endoplasmic reticulum (ER) is primarily involved in fatty acid elongation and desaturation, rather than the initial stages of fatty acid synthesis.

**Option C:** This option is incorrect because the peroxisomes are involved in the breakdown of fatty acids, particularly long-chain fatty acids, rather than their synthesis.

**Clinical Pearl / High-Yield Fact**
Fatty acid synthase (FAS) is a key regulatory enzyme in fatty acid synthesis, and its activity is tightly controlled by various factors, including insulin and glucagon. Inhibition of FAS has been explored as a potential therapeutic strategy for the treatment of obesity and metabolic disorders.

**Correct Answer:** C.