If your dishwasher backs up under the sink, it may indicate a plumbing problem. There may be a blockage in the dishwasher's drain pipe or a venting problem in the drain line, which prevents water from draining properly. This can cause water to back up under the sink.
To solve this problem, you can first check the dishwasher's drainpipe to make sure it is not clogged with food residue or other debris. If it is, you can clean the pipe by using a chemical drain cleaner or by dismantling it and cleaning it manually.
If the drain pipe is not the problem, there may be a blockage in the drain pipe. In this case, you can try using a plunger to unblock the pipe. If this does not work, it is recommended that you call in a professional to inspect the pipe with a camera and carry out a hydrocleaning to solve the problem.