What regions of north and south america show the greatest crustal activity?

The correct answer is - the western regions.

Both South America's and North America's western parts are located on places where there's heavy geologic activity, caused by the interaction of the tectonic plates.

The North American west experiences geologic activity because of the interaction of the North American plate and the Pacific plate, where the Pacific plate is subducting, thus having a convergent plate boundary, as well as because of the transform plate boundary between the North American plate and the small Juan de Fuca plate. Further south, the collision between the Cocos plate and the Caribbean plate occurs just of the western coast of Central America.

South America's western part is influenced by the convergent boundaries of the South American plate with the Nazca plate and the Antarctic plate, both of which subduct bellow the South American plate.