I downloaded a image, but forgot to favorite it, so can't find the author. Got the hash through.

If you have the MD5 hash of the image, you could either:
• Search md5:<your_md5_hash> on the posts page, or
• Go to e621.net/posts?md5=<your_md5_hash>

(Remember to replace the <your_md5_hash> part with your MD5 hash)

Alternatively to justfortheapi's answer, there's also a reverse image search - but the hash search should do just fine for this situation.

In addition to the already given answers, SauceNAO is also another way of finding the source of images you had downloaded or found.