1. **State the problem:** We have a rectangle WXYZ with diagonals intersecting at point P. Given that $WP = 4x + 6$ and $PY = 26$, find the value of $x$. 2. **Recall properties of rectangles:** In a rectangle, the diagonals are equal in length and bisect each other. This means point P is the midpoint of diagonal WY. 3. **Use the midpoint property:** Since P is the midpoint of WY, the segments WP and PY are equal. Therefore, we set: $$4x + 6 = 26$$ 4. **Solve for $x$:** $$4x + 6 = 26$$ $$4x = 26 - 6$$ $$4x = 20$$ $$\cancel{4}x = \cancel{4}5$$ $$x = 5$$ 5. **Conclusion:** The value of $x$ is 5.