without any details, its hard to provide anything other than a best guess on which alternator will fit/work.
From the pictures, it looks like it has black paint; so that infers the new engine is a Mercruiser product. without a serial number, the best thing you can do is look thru a catalog:
https://www.marineengine.com/parts/arco-marine-parts/
and see what your choices are.
The big driver is the case style needed to match the mounting hardware that's provided. There's really only a handful of choices...make some measurements and go from there.
you can also try ARCO's tech support department - they may be able to give you some hints...