Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 603: 15

The arrows indicate the direction of motion.

Since $t=2x$, substituting $t$ into $y$ gives $y=2(2x)^2=8x^2$. This is the equation of a parabola. As $x$ approaches $0$ from the left, $y$ is decreasing. The direction of motion is going down. As $x$ moves away from $0$ to the right, $y$ is increasing, so the direction of motion is going up.