"From" makes the most sense in this text, and that was my first inclination, but the first word given in the dropdown hints is "of" with "from" making no appearance in the list of hints at all. DL, if you're not going to accept your own hints, stop providing them. I'd just as soon look words up in an accurate dictionary and get it right.
I put "from" also but I think using "desde" here instead of "de" (so el would be there with desde) would mean "from". Can anyone confirm that? or would the sentence be the same as "desde el..." and "del..." From looking at some "de vs desde" info I think if you wanted to say you were from the other side of the street this might work (since de can be used to say where you're from) but if you wanted to say you threw the ball from the other side of the street you would use desde?!?!
In English, at least in the UK, there is a difference between "from the other side of the street", and "on the other side...". DL accepts both here - are both correct ? eg "I saw my friend ON the other side of the street". v. "My friend called to me FROM the other side of the street".