What type of extra flexible hoisting rope application is indicated for use?

The correct choice is 6x37. This type of flexible hoisting rope is specifically designed with a higher number of wires in its strands, which allows for greater flexibility and bending capabilities. In applications where the rope must navigate through pulleys or sheaves, having a rope that can flex more easily without kinking or losing performance is crucial.

The 6x37 construction consists of six strands, each containing 37 wires. This configuration balances strength and flexibility effectively, making it suitable for operations that involve continuous movement and repositioning. The additional wires in each strand contribute to the rope's flexibility, allowing it to work optimally in environments where frequent bending and looping occur.

Ropes with fewer wires per strand, such as the ones in the other options, typically offer more rigidity or are designed for heavier loads where less movement is required. Therefore, when high flexibility is paramount for the application, the 6x37 flexible hoisting rope is the best choice.