Changing binary counter structure such that increament and decreament methods will work in O(1) amortized
They may by suggesting that you use a binary counter with three digit values, $\{-1,0,1\}$, and budget a fixed additional time whenever you set a digit to $\pm1$.
To increment the counter you start at the least significant trit, and if it's $-1$ you set it to $0$ and stop, if it's $0$ you set it to $1$ and stop, and if it's $1$ you set it to $0$ and loop (using the previously budgeted time). Decrementing is the same with everything negated.