Let's analyze the given functions and statements:

1. Function A: $g(x) = -\frac{3}{2}x + 4$
   This is a linear function. Linear functions do not have maxima or minima, since they extend infinitely in both directions.

2. Function B: $f(x) = (x + 2)(x + 6)$
   Expanding this function:
   $f(x) = x^2 + 8x + 12$
   This is a quadratic function with a parabola opening upwards (since the coefficient of $x^2$ is positive). Therefore, it has a minimum point.

3. Graph C:
   The graph in C is a parabola opening downwards, indicating that it has a maximum point.

Now, let's evaluate the statements:

1. C has a maximum and A has a minimum.
   This is false because A (linear function) does not have a minimum.

2. B has a minimum and C has a maximum.
   This is true because B (quadratic) has a minimum and C has a maximum.

3. B and C have the same zeros.
   To check the zeros of B, we solve:
   $(x + 2)(x + 6) = 0 \implies x = -2, \, x = -6$
   For C, looking at the graph, the zeros seem different from B's. So, this statement is false.

4. A and B have the same y-intercept.
   The y-intercept of $g(x)$ is at $(0, 4)$.
   The y-intercept of $f(x)$ is at $(0, (0 + 2)(0 + 6)) = 12$.
   They are different, so this statement is false.

The correct statement is:
"B has a minimum and C has a maximum."

Do you want a deeper explanation or have further questions?

Related Questions:

1. How do you find the vertex of a quadratic function?
2. What is the general method to find the zeros of a polynomial?
3. How do you determine if a parabola opens upwards or downwards?
4. What are the characteristics of linear functions compared to quadratic functions?
5. How do you identify the y-intercept of a function graphically and algebraically?

Tip: Always check the direction of the parabola to determine if it has a maximum or minimum point.