If your vehicle is showing air blows from the wrong vents, here are the most likely causes and the parts you'll need to fix each one.
The small electric motor that moves the flaps inside the dash to direct airflow has burned out or its internal plastic gears have stripped. This is the most common cause of vent routing issues on modern vehicles.
Many older vehicles (and some specific modern trucks) use engine vacuum to move the vent doors. A cracked or disconnected vacuum hose will cause the system to default to the windshield defrost vents for safety. This is a very common error after recent engine repairs.
The climate control panel on the dashboard has failed internally and is no longer sending the correct electrical signals or vacuum routing to the actuators to change the vent modes.
If a vent actuator was recently replaced or the battery was disconnected, the HVAC system may need to undergo a specific electronic relearn procedure to know the physical limits of the vent doors.
The physical plastic flap inside the dashboard HVAC box, or the linkage connecting it to the actuator, has snapped. The actuator motor works, but the door itself cannot move. This requires extensive dashboard disassembly to repair.