Just bought Apple TV 4K Device. How do you charge the remote? I'm unable to use conventional line and also the cord that is connected to my iMac.

The remote is charged using a USB-C cable and a USB-C charger or a USB-C port on a computer.

If you don't have any charger with a USB-C port, you can buy a USB-C to USB-A cable to charge the remote using an existing USB-A charger you may have.

USB-A to USB-C cable:

mophie USB-A Cable with USB-C Connector (1 m) - Apple

USB-C to USB-C cable:

USB-C Charge Cable (2 m) - Apple

USB-C charger:

Buy 20W USB-C Power Adapter - Apple

Note that the charger and cable do not need to be Apple branded. They can be fro third party brands like uGreen, Anker etc...

They can be chargers from an iPhone or iPad you may already have etc...

Are you sure your cable is a USB-C cable?

Please see the images I posted above and compare them to your cable.

If they are the same, then you may have purchased a slightly older Apple TV, in which case the remote would use the iPhone style lightning cable instead of USB-C , so you can use a cable from an iPhone to charge it instead.

Also, identifying the exact model of Apple TV will help: click here ➡️ Identify your Apple TV model - Apple Support

See also:

Charge the Siri Remote – Apple Support (UK)

Phil0124 linked to specific cables that you can buy that will work.