1. **State the problem:** Harley needs twice as many biscuits as raspberries. Raspberries come in boxes of 12, biscuits in packets of 9. He wants no leftovers. 2. **Define variables:** Let $r$ = number of raspberry boxes, $b$ = number of biscuit packets. 3. **Express quantities:** Total raspberries = $12r$, total biscuits = $9b$. 4. **Condition:** Biscuits are twice raspberries: $$9b = 2 \times 12r = 24r$$ 5. **Simplify:** $$9b = 24r \implies 3b = 8r$$ 6. **Find integer solutions:** We want integers $r,b$ satisfying $3b=8r$. Rewrite as: $$b = \frac{8r}{3}$$ For $b$ to be integer, $r$ must be multiple of 3. 7. **Smallest $r$:** Let $r=3k$, smallest $k=1$ gives $r=3$. 8. **Find $b$:** $$b = \frac{8 \times 3}{3} = 8$$ 9. **Answer:** (a) Smallest boxes of raspberries: $3$ (b) Smallest packets of biscuits: $8$