From the Super Mario Wiki
The Mine-Cart Rail is a scrap found in Paper Mario: Sticker Star. Mario is required to retrieve it in Bowser's Snow Fort during the minecart ride by paperizing in any sticker to cause the minecart-riding Shy Guy carrying the scrap to crash into the resulting ? Block, allowing him to obtain it.
Mario must then keep moving across the rail, crossing one gap, then place the Mine-Cart Rail into the blank area at the next gap, allowing him to progress to the next set of rails.