car startes but cuts off when put in reverse or drive

Couple of reasons this can happen, first is an air leak or idle air control valve, You may have a vacuum leak, get a can of spray Throttle body cleaner, spray the vac lines and maniflod area, when the idle changes, youve found the leak! You want the engine running and spray on the outside but do direct the stream onto the hoses, if it is a vacuum leak, the engine idle will change speed, then you have detected a leak, repair the vacuum leak and see how it runs! If that doesnt do it, you may need a new idle air control valve, it's bolted to the throttlebody. Try to keep the spray off the hot exhaust manifolds, it can cause a fire. if no leak, the IAC may be bad. Second could the the torque converter may be locked up, do your brake lights work?