If your 4E engine turns off when you engage a gear, there could be a few potential causes for this issue. Here are a few possibilities to consider:

1. Transmission-related problem: One possible cause could be a problem with the transmission itself. It could be a faulty transmission sensor or solenoid, causing the engine to shut off when the gear engages. Additionally, worn-out clutch plates or a malfunctioning torque converter could also cause the engine to stall.

2. Engine misfiring: Another potential cause could be an engine misfire. A misfiring engine can cause loss of power and lead to stalling when the transmission engages. Faulty ignition components such as spark plugs, ignition coils, or fuel injectors could be the culprit.

3. Idle air control valve (IACV) issue: The idle air control valve controls the engine's idle speed. If it becomes clogged or malfunctions, it can cause the engine to stall when shifting gears.

4. Throttle body issues: A dirty or malfunctioning throttle body can disrupt the airflow into the engine, leading to stalling when the vehicle is put into gear.

5. Fuel delivery problems: Your engine may not be receiving sufficient fuel, which can cause stalling when engaging a gear. A clogged fuel filter or a malfunctioning fuel pump could be the cause.

To diagnose the exact cause of the issue, it is essential to have a professional mechanic perform a detailed inspection of your vehicle. They will have the necessary tools and expertise to diagnose and fix the underlying problem.