In Harry Potter and the Deathly Hallows, Hermione destroyed the fourth Horcrux by stabbing it with the Sword of Gryffindor.

The story behind the answer

False. Hermione did destroy a Horcrux in Deathly Hallows, but it was Hufflepuff’s Cup, and she used a basilisk fang in the Chamber of Secrets—not the Sword of Gryffindor. The sword was used by Dumbledore (Gaunt’s ring), Ron (Slytherin’s locket), and Neville (Nagini).

Memory tip: Basilisk venom destroys Horcruxes. Two tools carry that venom—actual basilisk fangs and the Sword of Gryffindor, which absorbed the venom when Harry killed the basilisk in Chamber of Secrets. So Hermione used the fang; the sword was wielded by others.