Problem figuring out the right flashcart

After going through three flashcarts, I'm done with all these Ebay sellers who have absolutely no idea how to work what they're selling or are just a parent of a eight year old and really just want to sell it.

Also yes I have seen "Which flashcart should I get" by Rydian. But because I'm not natively English, I sometimes just misunderstand things and I want to be really clear that the R4 I'm trying to get will work with my consoles.

I have two DSIs, one being a DSi XL 1.4.5e and the other...

Problem figuring out the right flashcart