The correct answer is: problem.
A bind is a difficult situation from which it is hard to escape. In this case, the state is facing a difficult problem that it is not sure how to solve.
The other options are incorrect because they do not accurately describe the situation. A conflict is a disagreement or argument, but the state is not disagreeing with anyone. A nuisance is a person or thing that is annoying or troublesome, but the state is not being annoyed or troubled by anything. Depression is a mental illness characterized by low mood, loss of interest in activities, and changes in sleep, appetite, and energy. The state is not experiencing any of these symptoms.
In conclusion, the correct answer is: problem.