The object of the puzzle is to rotate the column pieces so most of the lines between the pieces meet. With some pieces, not all of the lines match up. Left-clicking and dragging a piece will drag all pieces above it, so start solving the puzzle at the top. The lines of the top piece do match the lines on the second piece from the top. All but one of the lines on the second piece match with lines on the third piece. After that you'll have to experiment a little to find the closest fit.
So you'll NEVER get ALL lines to match up.
They only match up between the top two pieces.
Between 2nd and 3rd from top, all but one line will match.
But after that you just have to methodically look for the closest fit (the most lines matching), and if one arrangement doesn't work, try the next one.