Answer: B. $(0,4)$

Explanation:1. Identify the given equation: $y = 6x^2 + 3x + 4$

2. Understand what the y-intercept is: The y-intercept of a graph in the xy-plane is the point where the graph crosses the y-axis. This occurs when the x-coordinate is $0$.

3. Find the y-intercept by substituting $x=0$ into the equation: $y = 6(0)^2 + 3(0) + 4$ $y = 6(0) + 0 + 4$ $y = 0 + 0 + 4$ $y = 4$

4. The y-intercept is the point $(x,y)$ where $x=0$ and $y=4$. So the point is $(0,4)$.

5. Compare with the given options: - [A] $(0,3)$ - [B] $(0,4)$ (This matches our result). - [C] $(0,6)$ - [D] $(0,7)$

6. Conclusion: The y-intercept of the graph of $y = 6x^2 + 3x + 4$ in the xy-plane is $(0,4)$.