There was a ________ debate about the Middle East, then they moved to a vote.    lively    flexible    main    nimble

The correct word to fill in the blank is "lively."

In this context, "lively debate" suggests a discussion that is full of energy and enthusiasm, which fits well when referring to a debate about a complex and controversial topic like the Middle East.

The other options do not quite convey the same meaning in this context:

• Flexible implies adaptability but does not accurately describe the nature of a debate.
• Main suggests primary importance but does not pertain to the energy of the discussion.
• Nimble refers to quickness and agility, which is less relevant to the tone of a debate.

Thus, a "lively debate" is the most appropriate choice here.