For better understanding, try to identify what elements X and Y are:

Elements X with electronic configurations: 1s\(^2\)2s\(^2\)2p\(^4\) is Oxygen (Adding the electrons together as 2+2+4= 8)

Elements Y with electronic configurations 1s\(^2\)2s\(^2\)2p\(^6\)3s\(^2\)3p\(^1\) is Aluminium ( Adding the electrons together as 2+2+6+2+1 = 13)

When Aluminium being a metal reacts with Oxygen being a non-metal, there is a transfer of electrons from metals to non-metals as 3 oxygen atoms reacts with 2 Aluminium atoms thereby forming Al\(_2\)O\(_3\) ⇒ Y\(_2\)X\(_3\).