Hello @Nikhil29
Here's a support page with details on this: https://support.google.com/googlenest/answer/7215624?hl=en
In short, though, first set up the new Google WiFi unit in the house as a wireless mesh point. Once it's completely working there, connect it to the LAN Ethernet port on the primary Google WiFi unit (the one that's wired to your internet service through its WAN Ethernet port). You can't connect it to the same "outer" network your primary Google WiFi unit is connected to – it has to be part of the "inner" network created by the primary Google WiFi unit.
I would start with a test, using a short, known-good, Cat 5e Ethernet cable in the same room. Verify it shows as being connected "wired" in the Google Home app. Then, you can unplug it from Ethernet and power, and connect the long Ethernet cable to your garden building to the LAN port on the primary Google WiFi unit, and then connect the new secondary Google WiFi unit to the other end of that Ethernet cable in the outbuilding and power it up out there. If that long cable is working properly, it should come up and show as being "wired" in the Google Home app and provide WiFi access to clients in that area.
I personally like using inexpensive, unmanaged Ethernet switches to build a wired network in my home, and I would recommend buying a couple of 5-port Ethernet switches and installing one on each end of that long Ethernet cable. So, it would look like primary Google WiFi LAN port <-> switch-1 <-long-cable-> switch-2 <-> secondary Google WiFi point in outbuilding. These switches will help provide some electrical isolation, but if they have LED indicators for each port, they can also help diagnose issues with Ethernet cable connections.
