Hi there!
One of my students wrote ”Anime is popular Japanese culture. You will become to like it.”
I would say ”Anime is one of the most popular cultures in Japan. You will like them.” though, do you think it's okay?
I've never heard of the expression ”become to do”; so I searched about it though, some say it's okay but some say it's not correct.
And can we say ”popular Japanese culture”?
I think it should be ”Japanese popular culture” though.. Hmmm, I got confused 😅

See a translation

@Orangekingdom The most natural way to say this would be “Anime is a popular Japanese culture, and you will come to like it.” Your way of saying it is also completely acceptable and makes sense. I would not use “them”, however, as the subject of this sentence is singular (Anime).

“Become to do” is not a natural-sounding phrase, though I can understand what is meant by it. “Come to do”, “come to like”, and similar are great alternatives.
As for the adjective order, English is weird. There’s an unstated order that adjectives come in that even native speakers aren’t aware that they follow, but it sounds wrong when in the incorrect order. In this case, “popular Japanese culture” is correct.

Edit: the typical order of adjectives is as follows.
1) Quantity or number
2) Quality or opinion (good, bad)
3) Size
4) Age
5) Shape
6) Color
7) Proper adjective (often nationality, other place of origin, or material)
8) Purpose or qualifier