1. **State the problem:** Calculate the value of $\frac{120}{(32 + 8)} \cdot (32 - 8)$.\n\n2. **Apply the order of operations:** First, evaluate the expressions inside the parentheses.\n\n3. Calculate $32 + 8 = 40$.\n\n4. Calculate $32 - 8 = 24$.\n\n5. Substitute these values back into the expression: $\frac{120}{40} \cdot 24$.\n\n6. Simplify the fraction $\frac{120}{40}$. We can cancel common factors: $$\frac{\cancel{120}}{\cancel{40}} = 3$$ because $120 \div 40 = 3$.\n\n7. Now multiply: $3 \cdot 24 = 72$.\n\n**Final answer:** $72$