I found out the character name to an image I have. He's Yuzuki from Tamako Market. I want to watch the anime, but I don't know where to watch it.
I don't really know what websites that have anime to be honest.
Where can I watch Tamako Market?
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Not knowing where you live, it's not possible to give a definitive answer to where you can legally watch the show, but assuming you're in the US then it looks(1) like Tamako Market is available to stream on Hidive, for which you can either register an account with them or through VRV. As with most streaming services, it costs money to subscribe but you can get a 30 day free trial to start with. Hidive also runs in other countries, but licensing is a complicated business so it's best if you check for yourself.
If you would rather own a copy, then Tamako Market was licensed by Sentai Filmworks in the US, and they sell the DVD and Blu-Ray on their site or through retailers, although as an older title you may have to search around a bit to find a copy in stock.
(1) I say "looks" because I accessed the site from Australia, so it was probably showing me a different list to what someone in the US would see.