Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 603: 16

The arrows indicate the direction of motion.

Since $t=\frac{x-2}{4}$, substituting $t$ into $y$ gives $y=3+\frac{2 (x-2)}{4}=3+\frac{x-2}{2}=2+\frac{x}{2}$. This is the equation of a line. As $x$ moves to the right, $y$ is increasing. The direction of motion is going up. There is only one direction of motion.