p trap

Hi, I need to install a reverse osmosis system under my sink. It requires to drill and mount a waste water connection to the P trap. See images attached or video Relevant clip is at around 5:00. My P trap is different because of the washing machine and dishwasher waste hoses connecting to it...

in the process of fitting new plumbing for the kitchen waste. I read quite some opinions online of people who wouldn't fit bottle traps under a kitchen sink, but rather P trap or S trap. They claimed it fills up with gunk very quickly. I am not one of those people that uses a sink as an...