1. **State the problem:** We need to find the length of segment $YX$ in kite $WXYZ$. 2. **Recall kite properties:** In a kite, two pairs of adjacent sides are equal. Here, $WX = XY = 6$ and $WZ = ZY = 24$ (given or inferred from tick marks and segment lengths). 3. **Analyze given lengths:** Segment $WU = UY = 12$ and $UZ = 24$. Point $U$ lies on $WY$ such that $WY = WU + UY = 12 + 12 = 24$. 4. **Find $YX$:** Since $XY = 6$ (given as the vertical segment from $X$ to $U$), and $YX$ is the same segment as $XY$, the length $YX = 6$. 5. **Final answer:** $$ YX = 6 $$