This is the first puzzle in the Shadow of the Tomb Raider that's notably more challenging. It takes place in the Peruvian Jungle, shortly after finding Jonah near the airplane wreckage.
The location of the puzzle is presented in the picture above - the main characters have to lift the bridge and get to the other side of the precipice.
Go left of the bridge and climb up the wall to the tower. There is an interactive mechanism shown in the picture above. Using it will lead to opening the water flow.
Return to the bottom and take a look at another mechanism on the left of the bridge, shown in the picture. Lara and Jonah must cooperate here. Pushing the mechanism will cause water to flow into the green container.
The green container works as a counterbalance, but since it's punctured, you've got to hurry with the next step. Go back a little and take the path down to get under the bridge.
Aim the bow at the rope coil shown on picture 1. If you've shot it the right way, the rope coils will become linked (as shown on picture 2).
If getting under the bridge and shooting the coil takes too much time, the green container will run out of the water and you will have to repeat the entire sequence, starting from pouring the water into the container.
You can go back up and easily reach the other end of the bridge.