Translation:My younger brother likes to shower and sing at the same time.
"My little brother likes to bathe and sing at the same time."
淋浴 (Lin2 Yu4) is to shower, where I'm from.
Why are 'taking showers' and 'singing' inverted between Chinese and English?
一边A一边B means “while A, do B” (i.e. A is the background action in front of which B happens. But in English you can’t say “My younger brother likes [while taking a shower, singing]”, you have to move the “while” part to the end.
Because the singing is literally and figuratively an accompaniment (secondary) to the shower, the main or background activity. I believe the main activity is put first in Chinese. In English, however, the main activity can be put into a 'while' or 'when' clause, that goes last as a kind of background information, while the additional activity is fronted as newer, more interesting information.
I'm fascinated by the chinese sentiment (literally expressed by the language, anyway) that singing in the shower is a sort of multi-tasking.
In a shower you stand up while running water sprinkles down from above. A bath is a tub that you fill up with hot water and then you climb into. It's like a small pool.
What's wrong with "My little brother likes to shower and sing songs at the same time"?
The most idiomatic English way to say this would be "likes singing in the shower" but that would miss the point of the lesson. So taking that into account the best would be "likes singing while he's taking a shower".