To find the effect on Alexander's height each minute, we need to divide the total increase in height by the number of minutes.
The problem states that his height increased by 108 inches over 6 minutes.
So, we calculate:
\[ \text{Increase per minute} = \frac{108 \text{ inches}}{6 \text{ minutes}} = 18 \text{ inches per minute} \]
Therefore, the correct response is:
18 inches