I don't have enough information there to help you.
In order to connect to the Internet, your PLC must be connected to some form of router. Since the PLC only has a wired connection, the connection to the router will be wired. The PC appears to be connected wirelessly, but the PC's wired connection doesn't show a gateway, which tells me the wired connection isn't tied to the router.
Some wireless routers also have a built-in switch for wired connections. If so, that's where you need to connect. If there is a switch in the router, try connecting the PC to it and dumping the IP setup of the wired connection.