Göbekli Tepe stood from roughly 11,600 years ago to about 10,400 years ago, approximately 8,400 BC, a period of around 1,200 years.
The start date (~11,600 years ago) is accurate, but the end date and duration are off. Most sources place abandonment around 8,000–8,200 BCE, not 8,400 BCE, giving a span of ~1,400–1,600 years rather than 1,200.
UNESCO describes the site as active between 9,600 and 8,200 BCE, Wikipedia cites use until ~8,000 BCE, and multiple sources converge on a duration of roughly 1,400–1,600 years. Hancock's start date of 11,600 years ago (~9,600 BCE) matches well, but his end date of ~8,400 BCE (10,400 years ago) is roughly 200–400 years earlier than the commonly cited abandonment/burial date, and his 1,200-year duration is shorter than the scholarly consensus of 1,400–1,600 years.