Yeah: if you take apart the silver and black pieces, you can use the wrench on the inward-facing part of either piece.
I have this particular extractor and cannot (for the love of God) figure it out. So I remove the screw, put the black part into the crank, and turn the silver part towards (into) the hub and it’ll push the crank apart? Feeling pretty dumb here; someone with more mechanical talent please let me stand on your shoulders.
You remove the screw. The “black part” goes into the crank, I’d recommend greasing it beforehand, that will make it easier to remove. So you grease it a little, and screw it in the crank, as deep as you reasonably can. Then you can begin to turn the “silver part”, I never had a handle, always did it with an allen key (I hope it’s the right name in english :D). Just do it until it pulls the crank off, than remove the puller from the crank.
So the silver part pushes the crank off the hub? I must not be turning hard enough then. The handle is less than ideal because it cuts into your hand when pushing or pulling hard.
The important part is to make sure you get as many of the threads on that black part in there before screwing in the silver part. You want lots of grip so you don’t damage the threads. You could toss the handle that came with it and just use any old wrench that fits the hex part. The pullers I use are essentially just the black & silver part of yours.