The center of the circle is point upper O. Points upper S, upper R, upper Q,

Choice B is correct. Since $\stackrel{/mo>}{PR}$ and $\stackrel{/mo>}{QS}$ are diameters of the circle shown, $\stackrel{/mo>}{OS}$, $\stackrel{/mo>}{OR}$, $\stackrel{/mo>}{OP}$, and $\stackrel{/mo>}{OQ}$ are radii of the circle and are therefore congruent. Since $SOP$ and $ROQ$ are vertical angles, they are congruent. Therefore, arc $PS$ and arc $QR$ are formed by congruent radii and have the same angle measure, so they are congruent arcs. Similarly, $SOR$ and $POQ$ are vertical angles, so they are congruent. Therefore, arc $SR$ and arc $PQ$ are formed by congruent radii and have the same angle measure, so they are congruent arcs. Let $x$ represent the length of arc $SR$. Since arc $SR$ and arc $PQ$ are congruent arcs, the length of arc $PQ$ can also be represented by $x$. It’s given that the length of arc $PS$ is twice the length of arc $PQ$. Therefore, the length of arc $PS$ can be represented by the expression $2x$. Since arc $PS$ and arc $QR$ are congruent arcs, the length of arc $QR$ can also be represented by $2x$. This gives the expression $x+x+2x+2x$. Since it's given that the circumference is $144$, the expression $x+x+2x+2x$ is equal to $144$. Thus $x+x+2x+2x=144$, or $6x=144$. Dividing both sides of this equation by $6$ yields $x=24$. Therefore, the length of arc $QR$ is $2\left(24\right)$, or $48$.

Choice A is incorrect. This is the length of arc $PQ$, not arc $QR$.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.