Please see the following:
I assume that the repeat sign should refer back to the double bar line?
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The repeat should go back to the beginning, actually.
If the notation wanted to indicate going back to the double bar, they would have put an opening repeat barline. In the absence of such an opening repeat, the default is to return back to the beginning.
Alternatively, one could notate this with a dal segno marking, putting it at that double barline if that's where one is intended to return.
As the other answers say, music should be repeated from the beginning.
This is a simple arrangement of a melody by Prokofiev. It is preceded by 4 bars of chordal introduction. The double bar line separates the introduction from the main theme. The intention of the arranger is to repeat both the introduction and the theme.
It might be a good idea to learn the arrangement as it is, for educational purposes, but also to listen to original composition, recognize what was modified by the arranger, and possible change the arrangement to your liking.
The double barline after bar 4 shows the end of the introduction, and the beginning of the theme.Lacking any 'backward' repeat sign (!!:) means go back to the very beginning.
The way it's all written forms a big sandwich.
Intro.4 bars.Theme.8 bars.
Theme in another key.8 bars.(Repeat sign here):!!
Theme in another key.8 bars.