hello,

i am having troubles figuring out where the problem is under my kitchen sink. it doesnt seem to be draining correctly and is overflowing through the pipe the dish washer drains into.

There's a restriction in or below the lower tee fitting that needs to be mechanically clean. Don't use drain cleaning chemicals.

yean, loosen the kitchen sink tap adapter, remove the trap arm and stick a snake into that pipe to clear the clog..

What handyman installed that 'hodgepodge" of a drain? There should NEVER be an "open" drain pipe below the level of the sink "overflow" point. ANY "backflow" in the drain line is going to overflow the DW standpipe.

Are the fittings glued together with clear cement?

I see blue color up top at the AAV vent not sure if that's blue PTFE tape or Rain Or Shine cement.

just when you thought you've seen everything... there is a device call a dishwasher tail piece. this is used just below the sink basket strainer.

I thought it looked weird too when i moved in.

is my sink missing the dishwasher tail piece? i know nothing about plumbing.

I'd cut the horizontal branch off of that lower tee and put a rubber test cap on the stub. Then a 1 1/2" dishwasher tailpiece between the basket strainer and the trap, loop the dishwasher drain up to the underside of the countertop and clamp it there and drop down into the tailpiece.