1. **State the problem:** We need to multiply and simplify the expression for total weight growth per basket given by $$W(x) = D(x) \times R(x)$$ where $$D(x) = \frac{4}{x+2}$$ and $$R(x) = \frac{3x}{2x-4}$$. 2. **Write the expression:** $$W(x) = \frac{4}{x+2} \times \frac{3x}{2x-4}$$ 3. **Multiply the fractions:** $$W(x) = \frac{4 \times 3x}{(x+2)(2x-4)} = \frac{12x}{(x+2)(2x-4)}$$ 4. **Factor the denominator:** Note that $$2x-4 = 2(x-2)$$, so $$W(x) = \frac{12x}{(x+2) \times 2(x-2)} = \frac{12x}{2(x+2)(x-2)}$$ 5. **Simplify the fraction by dividing numerator and denominator by 2:** $$W(x) = \frac{12x \div 2}{2 \div 2 (x+2)(x-2)} = \frac{6x}{(x+2)(x-2)}$$ 6. **Final simplified expression:** $$\boxed{W(x) = \frac{6x}{(x+2)(x-2)}}$$ This expression models the total weight growth per basket in simplest form.