“in the eyes of Amnon it seemed impossible​.” This may have been because Amnon could not think of any legitimate way to be with Tamar since the Mosaic Law forbid brothers and sisters, even half-brothers and sisters, from having sex with each other (Lev. 18:6, 9; 20:17). However, since Amnon ignored those Mosaic Laws, it may have also been due to the fact that the unmarried daughters of the king would be closely guarded because any child they gave birth to would be a potential heir to the throne. Amnon may have felt it impossible to get to Tamar without her guardians, which eventually led to his ruse and his directly going to king David to send Tamar to him, which got rid of the guards.

“to do anything to her.” In this context, the phrase is euphemistic for sexual contact.