free software usb ethernet adapter?

I really don't think anyone can help you based on an image. Post the specs, or at the very least the model of the thingy.

It's looks like the one olimex is selling.

Actually I don't know if it's compatible with free/libre software but I know that olimex does not make 100% free software hardware.

For example I have found out that blobs are needed for the NAND to work same thing with mali, but that olimex does not explain it.

You can buy a usb to Ethernet adapter here (but they are currently out of stock)
and by using this link 25% of the money goes to the Trisquel project.
http://libre.thinkpenguin.com/

And you can look here they are already several ones that are sure to work

https://h-node.org/ethernetcards/catalogue/fr/1/1/undef/undef/yes/USB/ethernet-works/undef