What problem did Britain face at the end of the french and Indian war?

Answer 1

They suddenly controlled a significantly larger empire. They had taken control of most of Canada and India, but didn't have armies and infrastructure in place to either control or exploit these distant places.

In addition to that, the war had been very expensive. The French and Indian War was just a small part of a much larger war- the Seven Years War. In Europe, the Seven Years War saw Britain and Prussia fighting against Russia, France and Austria (there were other smaller countries, but those were the big ones). Prussia did most of the fighting in Europe in Britain's place; in return, Britain not only paid for their side of the war, but also paid most of Prussia's, so Prussia's brilliant king-general, Frederick the Great, could focus on fighting and not worry about bills.

So Britain suddenly had to deal with a much larger empire while somehow paying off their debts from war.