1. **State the problem:** Multiply and simplify the expression $4 w^3 \cdot 3 x^4 w^3 \cdot 3 x$. 2. **Write the expression:** $$4 w^3 \times 3 x^4 w^3 \times 3 x$$ 3. **Multiply the coefficients (numbers):** $$4 \times 3 \times 3 = 36$$ 4. **Multiply the variables with the same base by adding their exponents:** - For $w$: $w^3 \times w^3 = w^{3+3} = w^6$ - For $x$: $x^4 \times x = x^{4+1} = x^5$ 5. **Combine all parts:** $$36 w^6 x^5$$ 6. **Final answer:** $$\boxed{36 w^6 x^5}$$