I am doing this free test in http://test.mensa.no/
That, as far as I know, the only problem I can't solve.
Basically we shift the first row to the right. From first to second is easy transformation. We just turn the left and right side of the shape outward.
But then from the $2$nd row to $3$rd, I have no idea what the transformation should be.
What should it be?
I think the solution is the picture in the first row last shape.
As you see from first to second row you split the image in the middle and as you put it "turn it outwards" I would say mirroring it around its vertical middle axis. And from second to third row you take the right half of the picture mirror it again first by the vertical middle axis and then the horizontal middle axis.
Hope this helps :)