I'm trying to puzzle out the right stages in carrying out a BCNF decomposition. I discovered this situation, but I don't learn how to carry out the correct steps.

Schema = (A,B,C,D,E,F,G,H) FD's + P->F, G->G

Could someone show the right steps?

Determine a small cover making use of your FD's:

{A -> C, A -> G, A -> H, 
 B -> nothing, 
 C -> nothing,
 D -> nothing,
 E -> nothing,
 F -> nothing
 G -> nothing
 H -> nothing
 DE -> F}

Note AD -> C drops out because A alone determines C which suggests D is redundant within the FD (see Armstrong's Axioms - Augmentation).

3NF and BCNF definitions connect with dependencies about compund secrets. The only real compound key you've here's DE. Neither D or E take part in every other non-null FD's so getting rid of transitive dependencies and making certain that dependent characteristics depend around the 'key, the entire key, and absolutely nothing however the key' isn't an problem here.

Enter relations to ensure that the FD left hands side is paramount and also the right hands sides would be the non-key dependent characteristics of this key:

[Key(A), C, G, H]
[Key(D, E), F]

Now eliminate these characteristics in the cover, whatever remains are stand alone relations.

[Key(B)]

This ought to be in 3NF/BCNF