The image you provided seems to depict a quadrilateral with labeled vertices: $A(-3, 2)$, $B(2, 4)$, $C(4, k)$, and $D(-1, 3)$. From this setup, it's likely the problem involves finding the value of $k$ that satisfies certain conditions, such as ensuring the quadrilateral is a specific shape (like a parallelogram, rectangle, etc.).

To provide a detailed solution, could you clarify the exact question or condition related to this quadrilateral?

Here are some possible scenarios:

1. Are we supposed to find the value of $k$ that makes the quadrilateral a parallelogram?
2. Is $k$ supposed to satisfy a condition like the quadrilateral being a rectangle?
3. Is the question about finding the area of the quadrilateral for a given $k$?
4. Could the problem involve finding the slope of a line segment or proving that two sides are parallel or perpendicular?
5. Is $k$ related to the centroid, incenter, or another specific point of the quadrilateral?

Tip: When dealing with quadrilaterals, remember that opposite sides are equal and parallel in parallelograms, which can be a helpful condition for solving for unknowns.