You have a square taper bottom bracket. Actually an eccentric one, they are used to tension your chain. You should be able to use any square taper crankset. However, various cranksets require square tapers of different width. We cannot see the width of your BB, but one typically also changes the bottom bracket when changing the crankset and one just buys the width the crankset requires. The bottom bracket is much cheaper.
However, the Alfine crankset you mentioned uses a completely different kind of bottom bracket. It is a two piece crankset, the axle is integrated in the left crank and therefore you cannot use the old bottom brackets that include an axle.
Or choose one of the many square taper cranksets. There are many, there is little point to recommend a specific product. Just remember they require bottom brackets of a specific width.