The F20 error code means that your washer is not getting water. Do the following:
Check Flood Safe devices, if any, on the inlet hoses (see the first picture below). They could have shut off to prevent flooding, as they do from time to time. They can become quite a nuisance, so you’d better not use them on Kenmore washers.
Check water pressure in your water supply system. To do so, disconnect inlet hoses and put them in a bath, sink or bucket, and turn off the tap. If the flow is weak, the pressure is too low. It takes professional help to solve this problem. Contact your local water supply service.
If you see F20 on the display screen while the washer is filling properly, do the following:
Check the drain system. Not unlikely, the drain hose is not connected properly. Be sure that the drain system is set up as shown in the second picture below.
Check the opening in the upper part of the stand pipe: it should be open, so that air will flow through it. Do not push the drain hose more than 8” down this pipe.
Also, there may be leaks in the bottom section of the washer or hoses, a faulty water pressure switch, or a problem in the electronic control board, which often leads to false indications. Finally, in some Kenmore washers the error code appears when there is an issue in the heater system.