What are both the east and west coasts of Canada and the United States edged with: mountains or plains?
The best answer to this question is that both of these coasts are edged with mountains. The mountains are not necessarily right up next to the coast, but on both coasts, there are mountain ranges a relatively short way inland.
On the west coast of North America there is the coast range that runs all the way from Alaska down through British Columbia in Canada, and back into the United States where it can be found in Washington, Oregon, and California. Not far inland, there are the Cascade Mountains. These mountains are found in Washington, Oregon, and California. The Rocky Mountains are much farther inland in the United States, but they get relatively close to the coast in Canada.
On the east coast, the mountains are not nearly as impressive as on the west coast. These mountains are much older and have weathered down to where they are no longer very high. This mountain range is known as the Appalachians. It runs up the entire east coast of the United States and then into the Canadian provinces of New Brunswick, Newfoundland, and Quebec.
So, while the mountains do not necessarily touch the coast, it is still correct to say that both coasts are edged with mountains more than with plains.