Step 1: Understanding β-oxidation.
In β-oxidation, fatty acids are broken down into two-carbon units in the form of acetyl-CoA. For a fatty acid with \( n \) carbons, the number of cycles required for complete degradation is given by: \[ \text{Number of cycles} = \frac{n}{2} - 1 \] For palmitic acid (C\(_{16}\)), the number of cycles is: \[ \frac{16}{2} - 1 = 7 \, \text{cycles} \]
Step 2: Conclusion.
Thus, the correct answer is 7, as it takes 7 cycles of β-oxidation to fully degrade palmitic acid.