39
Reproductive cells are haploid (have 1/2 the chromosomes), whereas somatic/body cells are diploid (have the full set of chromosomes)
This makes sense if you think about it. Using the example from the question, every dog has 78 chromosomes. This includes two of each (there are two chromosome 1's, two chromosome 2's, etc. This is visible in the karyotype attached). One set of these chromosomes were inherited from the mother, and one set from the father. Each parent contributed 39 chromosomes (one chromosome 1, one chromosome 2, etc.). If the dog in the question were to have 78 chromosomes in its sperm cells, it would contribute two sets to its offspring. When combined with the chromosomes in the egg cell, the offspring would end up with extra chromosomes. Therefore, both the sperm and the egg cells will have 39 chromosomes, one of each. When combined, they will produce offspring with 78 chromosomes, the proper number.