lets use pictures to illustrate the crosses.
"pure" pharoah, brown, wildtype
Wh+Wh+Br+Br+yw+yw+e+e+pi+pi+

crossed with pure golden manchurian
Wh+Wh+Br+Br+YwYwe+e+pi+pi+

always equals?
Wh+Wh+Br+Br+yw+yw+e+e+pi+pi+
X
Wh+Wh+Br+Br+YwYwe+e+pi+pi+
=

Wh+Wh+Br+Br+Ywyw+e+e+pi+pi+
an "italian" a bird with one copy of the fawn gene (Yw), and no tibetan range gene "E"
when you cross the italians back to each other, you get wildtypes= no yellow gene, manchurians= 2 yellow genes and italians= 1 yellow gene
no lethal gene, provided you have a big enough breeding stock to not get dead-ended trying to get the yellow gene homozygous.
"pure" pharoah, brown, wildtype
Wh+Wh+Br+Br+yw+yw+e+e+pi+pi+
crossed with pure golden manchurian
Wh+Wh+Br+Br+YwYwe+e+pi+pi+
always equals?
Wh+Wh+Br+Br+yw+yw+e+e+pi+pi+
X
Wh+Wh+Br+Br+YwYwe+e+pi+pi+
=
Wh+Wh+Br+Br+Ywyw+e+e+pi+pi+
an "italian" a bird with one copy of the fawn gene (Yw), and no tibetan range gene "E"
when you cross the italians back to each other, you get wildtypes= no yellow gene, manchurians= 2 yellow genes and italians= 1 yellow gene
no lethal gene, provided you have a big enough breeding stock to not get dead-ended trying to get the yellow gene homozygous.