How did Carter show conservatism at home and idealism abroad?
Jimmy Carter was, generally speaking, relatively conservative on economic issues and relatively liberal in his foreign policy.
On economic issues, Carter took many steps that were more acceptable to Republicans than to Democrats. The most important of these, perhaps, were his steps to deregulate various industries. For example, it was Carter who deregulated the airline industry, allowing much more of a free market to exist ini that industry. That is a conservative action.
In foreign policy, Carter showed idealism by emphasizing human rights and general fairness. A major example of this can be seen in his handling of the Panama Canal. It was under Carter that the Canal was given to Panama on the idea that it really ought to belong to them. This is clearly an idealistic move because it gave up something that helped the US simply in order to be fairer to a foreign country.