The problem in your image gives the following information:

• The perimeter of quadrilateral WXYZ is 6 more than 4 times the length of side XY.
• You are provided with side lengths: $WX = 12$ and $ZY = 20$.
• You are asked to find $WZ$.

Step-by-Step Solution:

1. Define Variables: Let $XY = x$, the unknown side length.

2. Perimeter Formula: The perimeter of quadrilateral WXYZ is the sum of all its sides: $P = WX + XY + ZY + WZ$ Plugging in the given values: $P = 12 + x + 20 + WZ$ Simplifying: $P = 32 + x + WZ$

3. Use the Perimeter Condition: The problem states that the perimeter is 6 more than 4 times $XY$: $P = 4x + 6$ Set the two expressions for the perimeter equal to each other: $32 + x + WZ = 4x + 6$

4. Solve for $WZ$: Rearranging the equation: $WZ = 4x + 6 - 32 - x$ Simplifying: $WZ = 3x - 26$

5. Conclusion: The side length $WZ$ depends on $XY$. If you find $XY$ (which seems to be missing from the problem), you can plug it into the equation to find $WZ$.

Please check if the value of $XY$ is available elsewhere in the test. If it is not given, you cannot solve for $WZ$ numerically but the formula $WZ = 3x - 26$ will hold true.

Would you like further details or help in determining the value of $XY$? Here are 5 questions to deepen your understanding:

1. How does the perimeter formula change if more sides were known?
2. Why is rearranging the equation important in this context?
3. Could the problem be solved without knowing the perimeter condition?
4. How would the solution change if the shape of the figure were different?
5. What are the properties of trapezoids (like WXYZ) that might help solve such problems?

Tip: Always check if a problem gives all the necessary data before attempting a final calculation!