We have a Maytag Top loading washer purchased November 4, 2006 that will not agitage through any cycle (wash or rinse). Washer will fill with water …but will not wash. I can spin the water out.
Do you have any suggestions on how my husband could fix the washer? 
It is not clear from your post but it souns like it will spin ok, just not agitate. If it won’t spin or agitate check the lid switch. If it is ok, take off the front and see if
1.The transmission pulley will turn clockwise, if not the transmission is faulty.
See if the motor pivot spring and glides are ok. The motor is designed to move to act as a clutch. It probably does since your machine will spin.
Take off the belt and see if the motor turns in agitation mode. If not, check the wiring to the motor and the connection to the motor. Clean the connection with contact cleaner and reseat.
If everything checks out then the problem may be in the timer not sending the motor power to agitate.
See the service manual for how to do this.