"Own your shit" essentially just means "be honest." Let's break it into parts- it might be easier to understand that way. "Owning up (to something)" is a phrasal verb which means "admitting something." For example: "He made a huge mistake, but he still refuses to own up to it." Similarly, "owning (something)" can mean "admitting something/being open about something." For example: "If you're gay, just own it. No need to hide it." "Shit" literally means "poop" but in casual speech, it has a lot of other meanings as well. You can probably find more information about this online. In this case, it's a generic (if vulgar) noun that refers back to the Dan Brown novels. Let's take a look at the original again: "Oh, like the cereal guys buy when they're really there for condoms? Only makes it more conspicuous. Like, own your shit." If I were to translate this into simpler/more standard English, I might say: "It's like how guys buy cereal (at convenience stores) when they're really there for condoms. It only makes (the condoms) more conspicuous. If you're there to buy condoms, just be open about it." The guy they're criticized is embarrassed to be reading Dan Brown novels. A lot of people make fun of Dan Brown and people who like his books. So the guy is buying another book as well. The guys who are speaking think this is pathetic- if you like Dan Brown, just say so. No need to hide it.

Like is a filler word and doesn't really mean anything. This expert is about the person who goes into a shop to buy something embarrassing like condoms or a dirty magazine and they buy something else to cover up what they are really there for. Your shit is slang for the thing that you are really there for. It can be applied to your things in general or even attitude/ ideas - it is very flexible. It is normally applied to someone else's stuff not your own.

thank you so much

"Like" is an emphasis word when stating an opinion that you could replace with "What I'm saying is" or "I mean." People (especially girls) in Southern California in the 1980s would say the word "like" all the time and people called them "valley girls" (i.e., girls who live in the valley). "Like, the other day I was shopping, like, you know, just at the store down the street. And the girl I saw was like wearing a super short dress. And I was like, that's so short!" You can look up "valley girl" on youtube and see examples of people using the word "like" in this way. "Own your shit" means "be bold when you're doing something potentially awkward or embarrassing." Take ownership of the action instead of trying to hide it. Especially if you can't hide it anyway like buying something at a shop.