Feather color is inherited via codominant alleles, thus we will have either BB (black feathers), WW (White feathers, or BW (White with black spots).
Beak length is inherited via incompletely dominant alleles, thus we will have either LL (long beak), Ll (medium beak), or ll (short beak).
The parent cross: BBLl x BWLL
Normally when we look at two traits at once we will need a 4 x 4 Punnett square like in a true dihybrid cross AaBb x AaBb. This is because the parents can each produce four possible gametes so to see all the possible outcomes we need a large, 4 x 4 Punnett square. However, for this cross, even though we are studying two traits the situation is much more simple. The first parent can only make BL and Bl gametes and the second parent can only make BL and WL gametes, so we can actually use a 2 x 2 Punnett square.
Punnett square:
BL Bl
BL BBLL BBLl
WL BWLL BWLl
Results:
This cross can only produce birds with black feathers and long beaks (25%), black feathers and medium beaks (25%), white feathers with black spots and long beaks (25%), and white feathers with black spots and medium beaks (25%).
Phenotypic ratio: 1 black feathers and long beaks : 1 black feathers and medium beaks : 1 white feathers with black spots and long beaks : 1white feathers with black spots and medium beaks.