Actual hanging part at this timeloc.

As I think the film is located under the New Kingdom, we're faced with the problem in that capital punishments weren't very popular in the Middle to New Kingdom period: King Piya was very proud of the fact that he hadn't executed anyone and there seems a general aversion to killing people unless they're rebels - which was apparently a religious duty and then it was done with extreme prejudice, the point being to obliterate everything about the rebel. Often the manner of death isn't specified, but the most popular and well attested version is by burning, more specifically, burning by brazier - you were burned at the place of your crime on a specially made barbeque altar. The second most popular was by impalement. I can't find anything on hanging.

If you escaped the death penalty there was a wide variety of things that could happen -mutilations, loss of status, identity, forced labour, lose your property, or lose your office if you were an official.