What is the correct term for a backward handspring with a twist in gymnastics?

The correct term for a backward handspring with a twist is known as a BB gainer back handspring. In gymnastics terminology, the "gainer" refers to a movement where the gymnast performs a skill with a backward motion while also adding a twist. This type of skill often requires advanced technique and coordination as the gymnast not only has to control the forward rotation but also incorporate the twisting action.

The other options provided refer to different skills or movements. A straddle jump side represents a completely different type of jump, typically involving a takeoff and landing in a straddled position and is unrelated to the backward handspring concept. A press handstand (BB press HS) involves transitioning into a handstand starting from a standing or seated position, which differs from the dynamic action of a handspring. The 2-second hold indicates a position after performing a skill, such as a handstand, but does not denote the twisting action associated with a backward handspring. Therefore, the gainer back handspring is the only option that accurately describes the movement in question.