Answer-
![\boxed{\boxed{y=4}}](/tpl/images/0254/8156/5e0af.png)
Solution-
Properties of the diagonals of a rectangle,
The two diagonals are congruent (same length).Each diagonal bisects the other.Each diagonal bisects the other.
So using the first property, length of diagonal AC and BD will be same
![AC=BD](/tpl/images/0254/8156/a0430.png)
And using second property,
![BD=2\cdot BX](/tpl/images/0254/8156/c9d42.png)
Hence,
![AC=2\cdot BX](/tpl/images/0254/8156/4d797.png)
Given that,
AC = 4y  and BX = y + 4
Putting the values,
![\Rightarrow 4y=2\cdot (y + 4)](/tpl/images/0254/8156/e1f96.png)
![\Rightarrow 4y=2y + 8](/tpl/images/0254/8156/73cb3.png)
![\Rightarrow 4y-2y=8](/tpl/images/0254/8156/714f6.png)
![\Rightarrow 2y=8](/tpl/images/0254/8156/5eb7f.png)
![\Rightarrow y=4](/tpl/images/0254/8156/ae83b.png)
Therefore, y=4