I have a twin sink hooked with a garbage disposal and dishwasher. Recently th water in the sink with the garbage disposal fills up and the water does not flow through. When the garbage disposal turns on the water flows to the connecting sink. What could be the problem?

You have a blockage in the line inside the wall. Remove the "J" bend from the trap and send a snake up into the wall. You'll run into a bend about 8 inches in but once past that you only have 5 more feet to run out. Good luck, Tom

When the garbage disposal turns on the water flows to the connecting sinkThis occurs when the GD table's under water, The spinning table act like a centrifugal pump pumping water from one tub to the other.