Final answer:
The sitar is the long-necked lute with 24 movable frets, a characteristic feature that differentiates it from other stringed instruments like the banjo, oud, and mandolin.
Step-by-step explanation:
The instrument with a long neck and 24 movable frets described in the question is a sitar. This distinguishes it from the other options such as the banjo, which typically has a shorter neck with fewer frets and is known for its resonator back, giving it a unique sound.
The oud is a fretless instrument that is also plucked, while the mandolin has a much shorter neck compared to the sitar and typically has fixed frets. The sitar is a stringed instrument predominantly used in Indian classical music and is widely recognized by its long neck and the number of frets which allow for a range of microtonal adjustments.