According to translate.google.com:
In einer literarischen Karriere, die sich über rund 60 Jahre, Doris Lessing hat rund 50 Bücher, Gefühl, zu Hause in vielen verschiedenen Genres

For future note, please ask your questions entirely in english where possible. Again, Google reckons your German text is:
"I understand the second half of the sentence"

(and my vague knowledge of German concurs with that :-)

"To feel at home in many different genres" means she was comfortable working in many different categories (or styles of of literature or writing) during her career as an author which spread over 60 years.

"To feel at home" with something is when you are as comfortable and natural with something as you would feel when you when you are relaxing in your own home.