@Freesoul: But just because someone thinks it is correct doesn't make it correct. There are also degrees of "correctness", if you will. Some things are acceptable in speech that are not acceptable in writing - and things like e-mails are really written speech, not "writing" per se. (Did I make that clear?)
Even someone who totally supports descriptive grammar rather than prescriptive grammar would not accept a few instances of something as sufficient to declare it correct. In addition, when looking at Google, a thorough use of the search engine would require looking at every instance to see if the writer were a native speaker or not, whether the usage were a typo, or other reasons. In my own post earlier I was cutting and pasting, which led to an error I subsequently corrected.
As the user of a Google statistic I also warned about being careful with Google. If you type in a phrase, hits in the millions will indicate it is reasonably widespread. Hits of fewer than 1,000 are definitely suspect. When I typed in the initial phrase in question "Can you explain on this?" I got 15 Google hits, and several of those were from non-native speakers. "Can you explain this?" got 440,000 hits. Just based on the relative statistics, what would your conclusion be? Also, I would probably not have used Google had I not been posting in the forum a while and seen others doing it.
I am also aware that there are AE/BE differences - as well as AU and NZ and other dialects of English. That's why I asked in post #5 if a BE speaker had anything to contribute.
Since someone wrote "they're" for "their" would you now accept that as an alternative spelling? Or would you say that person erred? Lots of native speakers make that mistake; I see it in my students' writing all the time. It doesn't make it correct, however. Same thing with "explain on". I think you actually argued the case with your example. Think about it. :)
I'm not trying to pick on you, just thoroughly answer your questions.
BTW, I'm very tolerant of people's errors and variants in everyday life, but I start with the premise that in the Forum posters are asking about what is correct. I try to provide answers that are correct rather than "tolerated" depending on register or region. So, in answer to your original question I would have to say that "Can youi explain on this?" is not colloquial, just wrong.
Hope this helps!