1. **Problem statement:** Calculate the lateral area of a regular octagonal prism where the perimeter of the base is 24 cm and the height is one-fourth of the perimeter. 2. **Formula:** The lateral area $A_L$ of a prism is given by: $$A_L = \text{perimeter of base} \times \text{height}$$ 3. **Calculate height:** Given height $h = \frac{1}{4} \times 24 = 6$ cm. 4. **Calculate lateral area:** $$A_L = 24 \times 6 = 144 \text{ cm}^2$$ 5. **Answer:** The lateral area of the prism is $144$ cm², which corresponds to option (B).