1. The problem asks to identify the x-values where the function $f$ has a removable discontinuity. 2. A removable discontinuity occurs at a point where the function is not defined or has a hole, but the limit exists and can be "filled in" to make the function continuous. 3. From the graph description, there is a vertical asymptote at $x=0$, which is a non-removable discontinuity because the function tends to infinity or negative infinity there. 4. The graph also shows a hole (removable discontinuity) at the point $(6,3)$, meaning the function is not defined at $x=6$ but the limit exists. 5. There is no mention of holes or removable discontinuities at $x=-3$ or $x=-1$. 6. Therefore, the only removable discontinuity is at $x=6$. Final answer: $x=6$ (option C).