To find the distance Leah bikes in a training session after \( w \) weeks, we start with her initial distance of 8 miles. Each week, she increases her distance by \( \frac{3}{4} \) mile.
After \( w \) weeks, the total increase in distance will be \( \frac{3}{4} \) miles multiplied by \( w \) weeks, which is \( \frac{3}{4}w \).
The expression for the distance Leah bikes after \( w \) weeks can be formulated as:
\[ \text{Distance after } w \text{ weeks} = 8 + \frac{3}{4}w \]
Thus, the final expression is:
\[ 8 + \frac{3}{4}w \]