D.$123$ Pulses.
As in a $2^8$ Counter, the range would be from $0-255$. Hence to go from $10101100 (172)$ to $00100111 (39)$, the counter has to go initially from $172$ to $255$ and then from $0$ to $39$.
Hence to go from $172$ to $255, 255-172 = 83$ Clock pulses would be required. then from $255$ to $0$, again $1$ clock pulse would be required. Then, from $0$ to $39, 39$ clock pulses would be required. Hence in total $83+1+39 =123$ Clock pulses would be required.