Measurements on young children in mumbai, india, found this least-squares line for predicting height y from armspan x: y=6.4+0.93x all measurements are in centimeters (cm). how much on the average does height increase for each additional centimeter of armspan?

You're looking for a "rate of change" or "slope" here.  This slope is immediately evident in the given equation:  y = 6.4 + 0.93x:  it's 0.93.  If armspan increases by 1 cm, height on the average increases by 0.93 cm.

Change / increase = (slope)(increase in armspan)