What is the result of a hybrid black horse and brown horse?

Black is a color, not a breed or a hybrid of any kind.

Originally horses came in bay and a mutation occurred which allowed red and black to separate from each other. Black is connected to Agouti, and red (chestnut or sorrel) on extension.

How this works is that the two alleles at extension determine if black is a possible color, and the two alleles at Agouti controls where it is placed.

If a horse is ee at extension he's red, a red horse can have any Agouti status, but it will not show, but can be passed down to it's offspring unless it is aa, which means there is no Agouti present.

EE plus aa means that a horse is Homozygous (dominant) for black, Ee plus aa means the horse is Heterozygous (Recessive) for black.

EE, Ee, plus AA or Aa means the horse is bay with varying abilities to pass on Agouti, Black, and Red.