The long, hanging flaps on the back of a tuxedo jacket are called tails. Strictly speaking, a traditional tuxedo—or dinner jacket—does not have tails; the question is describing a tailcoat, whose defining feature is its extended rear sections.
Tailcoats developed from eighteenth- and early nineteenth-century coats that were cut away in front to make riding horseback easier. The remaining back portion formed two long panels that could hang behind the wearer. By the Victorian era, the dress coat had become formal evening wear, with tails typically reaching toward the knees and worn with white tie.
This creates a common mix-up in everyday language: people often call any formal black jacket a tuxedo, but a modern tuxedo is generally waist- or hip-length at the back. A jacket with long tails is more accurately a tailcoat or dress coat. “Tails” is nevertheless the standard, concise name for those hanging back sections, making it the canonical quiz answer.
The related morning coat also has tails, but they curve away gradually rather than being cut off squarely at the front. Both styles preserve the historical riding-coat influence in formal clothing.