Derek is middle-aged and is debating between staying home with his seven children or pursing his lifelong dream of using his engineering degree overseas to construct a new dam. According to Erikson's stages of psychosocial development, Derek's crisis most likely involves

generativity vs. stagnation

Explanation:

In the stage of generativity vs. stagnation a person who feels fulfilled in their home and the work place then the person has achieved generativity.

A person whose personal and work life is in turmoil then the person feels that is their life has become stagnant.

Here, Derek is choosing between his family and his career. He feels that his life will become stagnant if he does not pursue his career but at the same time he feels that his family would suffer consequences.

Hence, Derek is in the stage of generativity vs. stagnation.