When there are 9 people in the room, the mean height is 167.33cm. This means that the total height of all 9 people is 9 x 167.33cm = 1505.97cm
Then when one of the people leaves, there are 8 remaining in the room. The new mean height is 167.75cm. This means that the total height of all remaining 8 people is 8 x 167.75cm = 1342cm.
So the total height decreased from 1505.97cm to 1342cm when the person left the room. So she must have been 1342cm - 1505.97cm = 163.97cm tall.