Amodel rocket was launched from the ground and shot 150 feet straight up.it then fell back down to the ground and landed in the same place from which it was launched.which expression shows how far the rocket traveled?

The list of choices you included doesn't have any correct expressions on it.

-- If the rocket went straight up, and then dropped back at the same place
it was launched from, then it must have dropped straight down.

-- The route it followed on the way down was exactly the same as the
route it followed on the way up.

-- Since it reached a maximum height of 150-ft from the ground
and the route was straight, the length of the route was 150-ft.

-- (150-ft going up) plus (150-ft coming down)  =  300-ft traveled all together.

Diagonals must be congruent in a rectangle.