Estate taxes - Mistake?

For reading 22 and question 14, is that wrong? The equations for comparing a taxable gift has (1 - Tg) and (1 - Te) in the numerator and denominator.

It states that gift tax is paid by recipient (1 - Tg). Is (1 - Te) paid by the donor?

EOC 14 shows it (1 - Te) being paid by the niece and nephew.

BB18 shows it (1 - Te) being paid by the donor (Philip).

I don’t understand what or when to do what?