Eight values in order are 4, 6, x, 10, 12, 15, y and 22, where x lies between 6 and 10 and y lies…

Step 1. The value $x$. $Q_1 = \dfrac{6 + x}{2} = 7$, so $6 + x = 14$ and $x = 8$. It lies between 6 and 10, as it must.

Step 2. The value $y$. $Q_3 = \dfrac{15 + y}{2} = 17$, so $y = 19$. It lies between 15 and 22.

Step 3. The median. The 4th and 5th values are 10 and 12, so the median is 11.