The image shows a problem involving a quadrilateral with diagonals. To find the value of $x$, the equation for the diagonals' lengths is given:

• One diagonal has expressions $2(x + 6)$ and $24$.
• The other diagonal has expressions $4x$ and $24$.

Since these diagonals bisect each other in a parallelogram, we can set the two segments of each diagonal equal to one another:

1. For the first diagonal: $2(x + 6) = 24$ Solve for $x$: $2(x + 6) = 24 \implies x + 6 = 12 \implies x = 6$

Thus, the value of $x$ is 6.

Do you need further clarification or more details? Here are some related questions:

1. How can the properties of diagonals in parallelograms help solve problems?
2. What are other properties of diagonals in parallelograms?
3. Can you provide more examples where diagonals bisect each other in different quadrilaterals?
4. How would the solution change if the given shape was not a parallelogram?
5. What role does symmetry play in solving problems with diagonals?

Tip: Always check if diagonals bisect each other in quadrilateral problems—it simplifies calculations!