Answer
$\left\{\begin{array}{l}
x=2\cos t\\
y=2|\sin t|
\end{array}\right.,\quad t\in[0,4\pi]$
Work Step by Step
$\left\{\begin{array}{l}
x=r\cos t\\
y=r\sin t
\end{array}\right.,\quad t\in[0,2\pi]$
are parametric equations for a circle starting at $(r,0)$, tracing it once, counterclockwise.
For the upper half, $y\geq 0$, so we adjust the y-equation
$\left\{\begin{array}{l}
x=2\cos t\\
y=2|\sin t|
\end{array}\right.,\quad t\in[0,2\pi]$
This would trace the top half twice, from $(2,0)$ to $(-2,0)$ and back to $(2,0)$.
For another pair of tracings, we let $t$ assume the next $ 2\pi$ values, $t\in[0,4\pi]$.
So, finally,
$\left\{\begin{array}{l}
x=2\cos t\\
y=2|\sin t|
\end{array}\right.,\quad t\in[0,4\pi]$
