1. **State the problem:** Expand and fully simplify the expression $y(6y + 2) + 5(2y + 4)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. $$y(6y + 2) = y \times 6y + y \times 2 = 6y^2 + 2y$$ $$5(2y + 4) = 5 \times 2y + 5 \times 4 = 10y + 20$$ 3. **Combine the expanded terms:** $$6y^2 + 2y + 10y + 20$$ 4. **Simplify by combining like terms:** $$6y^2 + \cancel{2y + 10y} + 20 = 6y^2 + 12y + 20$$ 5. **Final answer:** $$6y^2 + 12y + 20$$ This is the fully expanded and simplified form of the given expression.