It looks like you're trying to connect a dishwasher drain to your sink's plumbing. The pipes under your sink include a trap (the U-shaped pipe) to prevent bad smells. The pipe that goes up and then down again is likely there to help water flow smoothly and avoid suction issues. Dishwashers typically drain into the sink's plumbing, often using an air gap (a device on the sink) or a high loop (making the drain hose go up high before it goes down to prevent backflow). You can use a special part called a dishwasher branch tailpiece to connect the dishwasher drain hose below the sink but above the trap. This part will help ensure that the drainage is done properly.
If the pipe going into the floor is another drain, you might be able to use it for the dishwasher. Make sure it’s a drain pipe and not something else, and check the local plumbing rules. Since your house has a slab floor, which can make plumbing changes tricky, it's a good idea to ask a plumber for help. They can make sure everything is set up correctly and follows the rules. Run the dishwasher to check for leaks and ensure proper drainage once connected.
