How did Phileas Fogg change the tough situation to his advantage?

Without knowing which tough situation this question is specifically asking about makes this question more difficult to answer. Fogg faces many tough situations and consistently figures a way out of it. That is what makes the book so fun to read and what makes Fogg such an unbelievably cool character. If I had to come up with the main way that Fogg changes tough situations to his advantage, I would say that it is through spending money, staying calm, and thinking creatively. An early example is when Fogg is riding the train in India, and he discovers that the railway is not finished. Passepartout is so enraged by the news that he is ready to punch someone, but Fogg calmly states that this problem was somewhat anticipated.

"Mr. Fogg, this is a delay greatly to your disadvantage."
"No, Sir Francis; it was foreseen."
"What! You knew that the way—"
"Not at all; but I knew that some obstacle or other would sooner or later arise on my route. Nothing, therefore, is lost. I have two days, which I have already gained, to sacrifice. A steamer leaves Calcutta for Hong Kong at noon, on the 25th. This is the 22nd, and we shall reach Calcutta in time."

Fogg then determines that he simply needs to find some kind of transportation that gets him to his destination by the time the steamer leaves. He does not have many options, and the option he decides upon is not cheap. Fogg is forced to spend a great deal of money on elephants as well as a guide, but he is not flustered by the situation. The elephant winds up being a solid form of transportation because it can take a shortcut that will gain Fogg twelve hours. These hours then allow Fogg to have time to rescue the princess.