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Here's a good clear explanation from Jack of Madras College.
Consider the movement of the block relative to the logs:
When the log makes one revolution it travels ${\pi}d$ metres. As the block is in contact with the logs, it moves ${\pi}d$ metres along the horizontal plane.
Therefore, the block moves ${\pi}d$ metres relative to the logs.
Now consider the movement of the logs relative to the ground:
When the log makes one revolution it rotates ${\pi}d$ metres. As it is in contact with the ground it moves ${\pi}d$ metres along the horizontal plane.Therefore, the log moves ${\pi}d$ metres relative to the ground.