This page of our guide to Anthem contains the solution for the barrier puzzle - you need to complete it during Triple Threat story mission. You solve the puzzle by picking up three correct colors near the giant gates. The full solution for this puzzle is below.
The puzzle's location
The barrier puzzle is shortly after you reach the Inner Chamber where you have to find Manifold. Before you focus on the puzzle, defeat three Dominion Valkyries.
After defeating the three enemies, approach the Manifold surrounded by a barrier. You learn that you need to deactivate it.
The puzzle's solution
There are three gates in the chamber (one of them is presented in the picture). Interact with them to change the color of the symbol located in the center of a gate. Your objective is to set the three symbols in the correct colors.
The solution is generated randomly, but this doesn't mean that the puzzle is complicated. You need to locate three tips regarding the colors. You can find these hints in any order - after reaching a gate, check the descriptions of the three possible tips to find the right symbol.
The first tip is a small symbol displayed on the wall near the bridge leading to the gates. Choose the same color on the nearby gate.
The second tip is a small symbol displayed on the high wall near the gates. Choose the same color on the nearby gate.
The third tip is a symbol displayed beneath the bridge leading to the gate. Choose the same color on the nearby gate.
Once all symbols are in their correct colors, the barrier will disappear. Take the Manifold to complete the mission.