In horses, black coat (b) is dominant over brown coat (b), and being a trotter (t) is dominant over being a pacer (t). a black horse who is a pacer is crossed with a brown horse who is a trotter. the offspring is a brown pacer. what is the genotype of the brown trotter parent

In order for a recessive trait to be apparent in an organism, the organism must receive a copy of the allele for that trait from both parents. 
Let the:
black coat: B
brown coat: b
Trotter: T
pacer: t

The offspring received both of the recessive alleles because it demonstrates the recessive phenotypes. Therefore, they genotype of the offspring is:
bbtt

The black horse that is a pacer that can produce this offspring will be:
Bbtt

Therefore, the brown horse's genotype must be:
bbTt

The offspring will receive b from both parents and t from both parents.