Here’s our guide on how to clear the cart puzzle in Shadow of the Tomb Raider:
Shadow of the Tomb Raider: Cart puzzle
Go straight ahead and push the cart down the ramp into the circular track disc in the middle. Walk down to the tracks and turn right where you will see a pulley. Go to the crank at the right hand side and turn the track disc until the white rope section of the cart is facing you.
Next, fire an arrow at the white rope and attach it to the pulley. Pull the cart as far up the slope as you can, then cut it loose and watch it clear a path.
A platform should then rise, and you will be able to see a rope ladder to continue your adventure.