What were the most difficult challenges faced by the plymouth and Jamestown settlers?

Lack of food and creating relations with the local Native American tribes.

Food supplies from the trip were low upon arrival and without established farming settlements, the English struggled to grow food and find food sources. The ground was difficult and different requiring new farming techniques.

To learn farming in the new world, settlers had to rely on relationships with Native Americans. This was difficult with language and cultural differences. Also the English had a long history of not wanting to work with other cultures and therefore would rather stay isolated from the tribes instead of integrate like the French and Spanish did.