To open the gate in Eye of the Serpent in Cenotes in Shadow of the Tomb Raider use a rope arrow to attach the pillar of the middle serpent to the pulley.
Turn the wheel on the pulley to swing the middle serpent to the right. Go up the path to the right and use the middle serpent to climb up to the top serpent. Clear the rubble around the base of the top serpent. Go back down to the pulley and use a rope arrow to attach the pulley to the top serpent. Move the top serpent so that it is letting water flow into the middle serpent.
Use a rope arrow to attach the pulley to the middle serpent and turn it all the way to the left so that it is letting water flow into the bottom serpent. If you need to use a rope arrow and the pulley to turn the bottom serpent so that it is letting water flow onto the wheel.
Make your way to the other side through the turning wheel in the middle of the area. Jump into the pool and clear the rubble at the base of the lower serpent. Use rope arrows and the pulley to adjust the position of the two serpents so that water flows onto the wheel.