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.

This means the log moves ${\pi}d$ metres relative to the
ground but the block moves ${\pi}d$ metres relative to the
logs.

Therefore, the block moves $2{\pi}d$ metres relative to the
ground, which is twice as much as the logs.

Thus:- the block
moves twice as fast as the logs .