Start by putting a penny on each of the frame/color combinations that is in the starting position.
A move consists of choosing a penny, seeing where its arrow points to, and placing there the penny that is in that column of your map.
With a bit of practice, you will find (for four-frame puzzles) that you only need three pennies - the one that you have just moved from is unnecessary. And this technique of using only three pennies makes the next move more obvious - it will usually be into the penniless column.
I hope that this is enough for you. There are no more hints. You will have to do the real work for yourself.
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