1. **State the problem:** Bethany has 4 1/2 cups of trail mix and wants to fill snack bags that each hold 3/8 cups. We need to find how many snack bags she can make. 2. **Convert mixed number to improper fraction:** $$4 \frac{1}{2} = \frac{9}{2}$$ 3. **Set up the division to find the number of bags:** $$\text{Number of bags} = \frac{\frac{9}{2}}{\frac{3}{8}}$$ 4. **Divide fractions by multiplying by the reciprocal:** $$= \frac{9}{2} \times \frac{8}{3}$$ 5. **Multiply numerators and denominators:** $$= \frac{9 \times 8}{2 \times 3} = \frac{72}{6}$$ 6. **Simplify the fraction:** $$= \frac{\cancel{72}^{12} \times 6}{\cancel{6}^{1} \times 1} = 12$$ 7. **Interpretation:** Bethany can make 12 snack bags. **Final answer:** $$\boxed{12}$$