Final answer:
The persuasive technique Johnny used is the foot-in-the-door technique.
Step-by-step explanation:
The persuasive technique Johnny used is the foot-in-the-door technique. This technique involves getting someone to agree to a small request or favor, and then following up with a larger request. In Johnny's case, he first asked his mother if they could spend the summer traveling through Europe, which his mother said no to. However, when he asked if they could go to Disney World instead, his mother said yes. By starting with a smaller request and getting his mother to agree, Johnny increased the likelihood of getting his larger request granted.