We cannot pull up our watch if the small or large hand is between 3 and 4, or 8 and 9. How much time is there in a day when we can pull up the watch?
The hour hand stays between the 3 and 4, and between the 8 and 9 for 1 hour each, over a period of 12 hours, making it impossible to wind the wall clock for 120 minutes. In the remaining 10 hours, the hour hand passes between the 3 and 4, and between the 8 and 9 for 5 minutes each hour, totaling an additional $10 \cdot 10=100$ minutes, during which the wall clock cannot be wound either. The same situation applies in the next 12 hours. In the remaining time, that is, $1440-2 \cdot(120+100)=1000$ minutes, it is possible to set the clock, which amounts to 16 hours and 40 minutes daily.