LAN

You need to provide more details.

Type of xbox?

Are you plugging directly into a gateway or router or modem?

Have you tried a different ethernet cable?

Does WiFi work?

Hi there,

as far as I know you can't directly connect your console to a different console with a ethernet cable and play together, you will have to use at least a hub (or switch) that allows you guys to connect to the same network and possible required to connect
to Xbox Live etc and then play together via Live.

Since you both will be on the same network, it might require some additional setup, which may be dependant on the networking hardware used.

Let us know the results

Could it also be possible you're using the wrong type of cable, such as a cross over or straight. Also your router might not be setup to assign DHCP, so you might have to assign a static IP to the Xbox

maybe you have issue with cord

The ethernet cable is probably defective.
Alternatively, try to set a static IP on the console (Settings->Network Settings->Advanced settings->IP settings->Manual) keeping in mind the gateway assigned by the router. Usually it is 192.168.0.1, so the settings could be:
- IP address: 192.158.1.100
- Subnet mask: 255.255.255.0
- Gateway: 192.168.0.1 (IP of router)
- Primary DNS address: 8.8.8.8 (google)
- Secondary DNS address: 8.8.4.4 (google)