Long story short, I renovated my kitchen and have two counters.
I have a counter where the oven and kitchen sink reside. Across from the counter (about 5 ft), I have a dishwasher across. I have a drainage tube (rubber hose) that runs from the dishwasher to the sink (about ~8-9ft long). Whenever I try to drain, the water just stays there and does not drain. 
I took out the drainage hose and was able to drain the water in the dish washer in a bucket (through the dishwasher's drain cycle).
When I bought the dishwasher, I was assured that the pump was strong enough to pump the water and the drainage pump will continue to pump as long as there is water in the dishwasher.
I think the dishwasher is not draining due to the distance that the water has to travel to drain (I checked for clogs, there are none).
I am guessing I messed up big time and may need to custom fit my dishwasher with a much stronger pump? I'd greatly appreciate any advice or words of wisdom.
Best Answer
I can only think of three options here...
Water flows downhill
The first (less optimal) option, is to raise the discharge up and allow it to flow down to the drain connection. In this scenario, you'll want to have the discharge tube go up to an air admittance device (AAV) or air gap. From there it should flow downhill (1/4" per foot), until it reaches the garburator connection.
Use a separate drain
The other option, is to discharge the dishwasher to its own drain. Install a properly vented standpipe near the dishwasher, and connect the discharge tubing to that (follow local plumbing codes).
Go under the floor
The last option is to run a drain line under the floor, and attach to the sink drain below the floor. Install a trap near the dishwasher, and run a proper drain that tees into the sink drain (follow local plumbing codes).