GE washer fills, then drains
Right off the top, "motor or control" + "fills" + "one or two rotations" + "drains" indicates a problem with the drum motor. Since it fills and drains, it is unlikely to be related to hoses, filters, inlet valve, etc.

I found a site that explains how to get into Service Mode. This should enable you to do some more diagnostics. Another page on that site describes the E46 error as follows:


  E42/E48/E49/E46/E54 Motor Related Errors
  
  These three errors are motor errors and can be caused by a bad inverter or motor. First, clear the code, exit the service mode and disconnect the power to the washer for at least 30 seconds. Don’t disconnect the power until you exit the service mode because it may damage the control. If the problem persists see the page below. 


So that points to:


Inverter
Motor
Something causing the motor to overload. Since it does "one or two rotations", the motor is getting at least some power (inverter) and is not totally dead (motor). It could be wearing out or malfunctioning in some way that it either draws too much power (and the control board senses that and shuts down) or doesn't turn fast enough or turns too fast (e.g., if pulley is loose) (and the control board senses that and shuts down).


So next steps (aside from anything you can figure out in Service Mode) is going to be to disassemble it to check the motor for loose connections (doubtful, but you never know), dirt blocking the motor or similar "easy fixes". One likely culprit is the drive belt (part WH08X10048) - if that is worn out it could explain everything, though even that is in the $50 range so you want to be fairly certain that is the problem before ordering one.

If that doesn't turn up anything, then you get into "swap components" mode. The catch is that a motor assembly (part WH20X10028) ranges (currently, subject to change, which is why we don't do "shopping questions") $50 to $300 or more depending on where you get it from, new/used, etc. In which case it may be time to look for a new washing machine.