12) $$ \left(6 x^{2}+4 y+6\right)(y+4)= $$

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To expand the expression $$ \left(6x^{2} + 4y + 6\right)(y + 4) $$, we'll distribute each term in the first polynomial by each term in the second polynomial.

1. **Multiply each term in the first polynomial by $$ y $$:**
   $$
   6x^{2} \cdot y = 6x^{2}y
   $$
   $$
   4y \cdot y = 4y^{2}
   $$
   $$
   6 \cdot y = 6y
   $$

2. **Multiply each term in the first polynomial by $$ 4 $$:**
   $$
   6x^{2} \cdot 4 = 24x^{2}
   $$
   $$
   4y \cdot 4 = 16y
   $$
   $$
   6 \cdot 4 = 24
   $$

3. **Combine all the results:**
   $$
   6x^{2}y + 4y^{2} + 6y + 24x^{2} + 16y + 24
   $$

4. **Combine like terms:**
   $$
   6x^{2}y + 24x^{2} + 4y^{2} + (6y + 16y) + 24
   $$
   $$
   6x^{2}y + 24x^{2} + 4y^{2} + 22y + 24
   $$

**Final Expanded Form:**
$$
6x^{2}y + 4y^{2} + 24x^{2} + 22y + 24
$$

**Answer:**
After expanding, the expression is 6 x²y + 4 y² + 24 x² + 22 y + 24
The expanded form of $$ \left(6x^{2} + 4y + 6\right)(y + 4) $$ is $$ 6x^{2}y + 4y^{2} + 24x^{2} + 22y + 24 $$.

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