"pénétrer" is usually used for objects going through something else, like a knife through the flesh for example, or water through earth. It has pretty much the same meaning as the English verb "to penetrate", except maybe for a few figurative meanings.
If the correct answer is intended to be "Je penetre," then Duolingo should please add that into the definition for "enter." As it is, with "J'entre" being shown as a valid definition that's then marked as incorrect, this practice is very misleading and frustrating.
I keep writing this as Je entre, can someone maybe give me tips on how to remember that it's j'entre? I get contractions right most of the time, but this one just won't stick no matter how many times I enter it wrong.