The author says the lady failed to see that if liberty let her walk down the middle of the road, it would equally let a taxi-driver drive on the pavement, and that unchecked liberty ends in chaos. So she failed to realise that her liberty was not unlimited. The other options describe things she may or may not have known, but they are not what the author says she missed.
Why each option is right or wrong
(a) Wrong. The author's point is about limits on liberty, not whether she was free.
(b) Right. Her liberty was not unlimited.
(c) Wrong. Her being old is not what she missed.
(d) Wrong. The author does not say roads are only for motor vehicles.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.