I need to know if the reduction in the pictute is ok or if it's a mistake.

I've marked it red.

thanks!

 

I 'm afraid not. Try to work it from the other side to confirm it:

(B XOR D)'(A XOR C)'=
(BD+B'D')(A XOR C)'<>BD+B'D'(A XOR C)'

Care to give it another try?