1. **State the problem:** Given $x=2$, $y=3$, and $z=-4$, find the value of the expression $$2xy + y^2 + 3x$$. 2. **Write the formula:** The expression is $$2xy + y^2 + 3x$$. 3. **Substitute the values:** Replace $x$ and $y$ with their given values: $$2 \times 2 \times 3 + 3^2 + 3 \times 2$$ 4. **Calculate each term:** - $2 \times 2 \times 3 = 12$ - $3^2 = 9$ - $3 \times 2 = 6$ 5. **Add the results:** $$12 + 9 + 6 = 27$$ 6. **Final answer:** The value of the expression is $27$.