1. **State the problem:** Simplify the expression $$(2x^2 + yx^2)(3x^2 + 3x^2).$$ 2. **Combine like terms inside the parentheses:** $$3x^2 + 3x^2 = 6x^2.$$ So the expression becomes: $$(2x^2 + yx^2)(6x^2).$$ 3. **Factor out $x^2$ from the first parentheses:** $$2x^2 + yx^2 = x^2(2 + y).$$ 4. **Rewrite the expression:** $$x^2(2 + y) imes 6x^2 = 6x^2 imes x^2 (2 + y).$$ 5. **Multiply the powers of $x$:** $$x^2 imes x^2 = x^{2+2} = x^4.$$ So the expression is: $$6x^4(2 + y).$$ 6. **Distribute $6x^4$ over $(2 + y)$:** $$6x^4 imes 2 + 6x^4 imes y = 12x^4 + 6yx^4.$$ **Final answer:** $$12x^4 + 6yx^4.$$