We haven't made the leap to Creative Cloud, but I have a client that is using a font that is located in Typekit. Am I able to use fonts in Typekit with my CS6?
You’ll have to pay for a TypeKit subscription.
Yes, you can use Typekit sync fonts with CS6 and other desktop programs. You'll need to install the free Creative Cloud app to do so, and also select a Typekit plan here: Pricing | Typekit
Here's an article that explains more about font sync and how to use it: How to sync fonts
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