If by chance you have a coax cable anywhere near the garage (maybe a cable box in an adjacent living room?) you can get a coax splitter, split that connection, and buy a moca adapter for $20-50 off amazon. This converts coax back to ethernet. Theres a few dependencies here:
You are using a FiOS router with MoCA/coax connected
or
Buy two moca adapters and attach one to ethernet and coax at your router, and the second to the split line running to your garage.
MoCA 2 adapters can do up to 500mbs, and MoCA 2 bonded adapters can do up to 1gbs. I believe MoCA 2.5 can do 2 or 2.5gbs, but that would exceed your internet speed anyway. It would only be useful if you have significant internal traffic, like an internal media server that feeds clients without needing to go out to the internet.
I've used MoCA adapters throughout my home to "hardware" endpoints and have been very pleased with them, and MoCA seems to tolerate a significant amount of splitting and varying cable qualities unlike gigabit ethernet.
Keep in mind the cable run length limit for ethernet CAT6 is 328 feet. I'd imagine that's more than enough but still something to keep in mind when running your cable.
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