To find the increase in Alexander's height each minute, we can divide the total height increase by the amount of time in minutes.
Given that Alexander's height increased by 108 inches over 6 minutes, we calculate:
\[ \text{Increase per minute} = \frac{\text{Total Increase}}{\text{Time}} = \frac{108 \text{ inches}}{6 \text{ minutes}} = 18 \text{ inches per minute} \]
Therefore, the effect on Alexander's height each minute is 18 inches.