In the first part of the experiment there were only a few colonies on the streptomycin positive plate. In this second part there are a large number of colonies on the streptomycin positive plate that was inoculated with the antibiotic resistant strain? What is the most likely explanation for this difference?

The antibiotic generated a selection pressure on the strains, and only those with the antibiotic resistance gene survived. This feature is inherited in the next generation.

In the first part, the objective of the experiment was to select those strains that were resistant to the antibiotic. They are those that in the first part had greater reproductive success, so they could generate colonies, while many other colony-forming units (CFUs) could not survive, so they did not generate colonies. The strains selected in the first stage were again inoculated in a medium with the same antibiotic, and indeed, they had no problem in reproducing, since all the CFUs had already inherited the antibiotic resistance character. That's why more colonies are seen in the second experiment.