There is a mistake in your writing
:The similar triangles should be ABE (& not ABD as you stated) & ACD
If so, we can write the following proportion:
AB/AC = BE/CD.
We know that AB =10, BE=4, AC= 10 + BC (BC =12, Given), so AC =22
Plug into the above: 10/22 =4/y===> y= (22 x 4)/10===> y =44/5 =8.8
