What did Charles dickens teach himself after buying brachgraphy?

There seems to be a misunderstanding in your question. Charles Dickens did not buy "brachgraphy." It's likely you are referring to brachygraphy, a shorthand system that was popular in the 19th century. However, there's no evidence that Dickens actually learned this system.

While Dickens was known for his fast writing and ability to produce voluminous works, his main shorthand system was "phonography", which was developed by Isaac Pitman. He used this system throughout his life, particularly in his early days as a reporter.

It's important to be careful with terminology when researching historical figures. A slight spelling difference can lead to confusion!