First of all lets make a point clear what is x!=y,
if x=y then it could be X^2n or Y^2n and we know we can easily say it’s a Regular beacause we are seeing
pattern of Arthmetic progression (aa,aaaa,aaaaaa,aaaaaaaa) so it will always be CFL beacause every regular is also a CFL.
But they said x!=y, so x^my^n,where m!=n beacause they give that number of x is not equal to number of y
as we know we can draw pda for x^my^n where m=n taking a complement of that will not satisfy
beacause in CFL complement of CFL may or may not be CFL,
So we have to think in other way |X|!=|Y| which means |X|>|Y| or |X|<|Y|
we know union of two CDL is also a CFL,so we can make CFL for |X|>|Y| and |X|<|Y| and union them so we Can say given launguage is CFL.