(b) 20 cm
By Basic Proportionality Theorem, since PQ ∥ BC:
$$\frac{AP}{PB} = \frac{AQ}{QC} \Rightarrow \frac{4}{6} = \frac{8}{QC} \Rightarrow QC = 12 \text{ cm}$$
$$AC = AQ + QC = 8 + 12 = \mathbf{20 \text{ cm}}$$
Source: Chapter 6, Theorem 6.1 (Basic Proportionality Theorem)
Apply BPT: since PQ ∥ BC, the line divides AB and AC in the same ratio → AP/PB = AQ/QC. Solve for QC, then add AQ + QC to get AC. A common mistake is giving QC (12 cm) as the answer instead of the full length AC (20 cm).