To find Selma's unit rate in miles per hour for her Monday run, we first need to calculate her speed in miles per hour.
The total distance she ran is \( \frac{3}{4} \) of a mile, and the time it took her is \( \frac{1}{6} \) of an hour.
To determine her speed in miles per hour, the formula to use is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values we have:
\[ \text{Speed} = \frac{\frac{3}{4} \text{ miles}}{\frac{1}{6} \text{ hour}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \text{Speed} = \frac{3}{4} \times \frac{6}{1} \]
Calculating that gives:
\[ \text{Speed} = \frac{3 \times 6}{4 \times 1} = \frac{18}{4} = 4.5 \]
Therefore, Selma's unit rate is \( 4.5 \) miles per hour.
The final answer is:
\[ \boxed{4.5} \text{ miles per hour} \]