Translation:Can I come with my friend?
It is grammatically incorrect because the pronoun "me" cannot be used as the subject of a verb (you need to use "I"). You should also always place the third person (my friend) before yourself, so it should be "My friend and I" not "Me and my friend" if you want to be grammatically correct.
It is very frustrating that Duolingo is so picky on translations with Mandarin! On this phrase I translated it as "May I come with my friend?" and I was marked wrong because the answer is supposed to, "Can I come with my friend?" Maybe my English is not good enough either but to me both would appear to be reasonably acceptable translations.
If I'm completely out in left field please let me know what is the difference!