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The washing machine will have two states: washing which required a counter that will stop when it reaches number 6 and drying which required a counter that will stop when it reaches number 4. The controller should have 2 inputs a start and a reset. When the start input is disabled (set to 0), both washer and dryer should stop. When the start input is enabled (set to 1), the washing cycle should start counting from 0 to 6 then stop; after that the dryer cycle should start counting from 0 to 4, i.e., the drying cycle will start after the washing cycle finish. The reset button we reset both counters. The final circuit will look something like this

washing machine controller