Literally this says "All (bütün) women (kadınler) are behind me (benim arkamda)" yes? In english you would literally say this "All women are behind me" and in context it would mean 'all women support me'. But 'support' and 'behind' are 2 different words. And that would be the figurative understanding but not the literal word. So does 'arkamda' literally mean behind and support?
*arka" literally means "the space not in front of you" or "behind." It is a noun that is used as a postposition and is called a Type 1 postpostion.
With this being said, it kind of literally says "all women are behind me" in the non-literal sense and literal sense. One has to ask "who are they behind?" The answer is "me" so it will take the 1st per. sing. possessive ending "arka-m."
Now we need the locative to describe location. They are "at my back" and not moving towards or away from it. For this reason, you must use the locative. Arkam does not end in a vowel, so there is no buffer -n- needed. So you end up with "arkamda."
If you wanted to use other people (say "you" or "her") it would be arkanda (2nd person) or arkasında (3rd person) :)
After and Behind are slightly different in English. Behind is more static than After. Behind means "At your back". After, on the contrary, gives the idea of position in movement. You go somewhere and the women follow you. After can give the idea of following with a purpose. Behind gives the idea of just position like in "They are coming behind me", or "I am coming and they'll follow behind". In its other sense, Behind gives the idea of authorship, support or support group. "Who is behind all this?" meaning who supports this idea or who is the author of this idea. They are behind you = They support you. Or you are their voice, but they are the authors of the idea that you are voicing. Prepositions can be tricky in any language. It took me several graduate courses on prepositions to get to understand their dynamic. This is why I don't get it when the system returned my answer as wrong.
All women support me =
- Bütün (tüm) kadınlar beni destekler (destekliyor)
- Bütün (tüm) kadınlar benim arkamda
- Bütün (tüm) kadınlar benim yanımda
- Kadınların hepsi (not specific, all of them) beni destekler/destekliyor (benim yanımda/benim arkamda).
Everyone is correct translation.
Why behind and not after? I think we are in the presence of an idiom. Idioms CANNOT be translated literally.
This supports my previous comment. To me behind here makes no sense.